List of space groups – Wikipedia

By hassandigitaljhb@gmail.com / February 1, 2026

Number Point group Orbifold Short name Full name Schoenflies Fedorov Shubnikov Fibrifold (primary) Fibrifold (secondary) 16 222

222

P222 P 2 2 2

\Gamma _{o}D_{2}^{1}

9s

(c:a:b):2:2

(*2_{0}2_{0}2_{0}2_{0})

17 P222₁ P 2 2 2₁

\Gamma _{o}D_{2}^{2}

4a

(c:a:b):2_{1}:2

(*2_{1}2_{1}2_{1}2_{1})

(2_{0}2_{0}{*})

18 P2₁2₁2 P 2₁ 2₁ 2

\Gamma _{o}D_{2}^{3}

7a

(c:a:b):2

2_{1}

(2_{0}2_{0}{\bar {\times }})

(2_{1}2_{1}{*})

19 P2₁2₁2₁ P 2₁ 2₁ 2₁

\Gamma _{o}D_{2}^{4}

8a

(c:a:b):2_{1}

2_{1}

(2_{1}2_{1}{\bar {\times }})

20 C222₁ C 2 2 2₁

\Gamma _{o}^{b}D_{2}^{5}

5a

\left({\tfrac {a+b}{2}}:c:a:b\right):2_{1}:2

(2_{1}{*}2_{1}2_{1})

(2_{0}2_{1}{*})

21 C222 C 2 2 2

\Gamma _{o}^{b}D_{2}^{6}

10s

\left({\tfrac {a+b}{2}}:c:a:b\right):2:2

(2_{0}{*}2_{0}2_{0})

(*2_{0}2_{0}2_{1}2_{1})

22 F222 F 2 2 2

\Gamma _{o}^{f}D_{2}^{7}

12s

\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):2:2

(*2_{0}2_{1}2_{0}2_{1})

23 I222 I 2 2 2

\Gamma _{o}^{v}D_{2}^{8}

11s

\left({\tfrac {a+b+c}{2}}/c:a:b\right):2:2

(2_{1}{*}2_{0}2_{0})

24 I2₁2₁2₁ I 2₁ 2₁ 2₁

\Gamma _{o}^{v}D_{2}^{9}

6a

\left({\tfrac {a+b+c}{2}}/c:a:b\right):2:2_{1}

(2_{0}{*}2_{1}2_{1})

25 mm2

*22

Pmm2 P m m 2

\Gamma _{o}C_{2v}^{1}

13s

(c:a:b):m\cdot 2

(*{\cdot }2{\cdot }2{\cdot }2{\cdot }2)

[{*}_{0}{\cdot }{*}_{0}{\cdot }]

26 Pmc2₁ P m c 2₁

\Gamma _{o}C_{2v}^{2}

9a

(c:a:b):{\tilde {c}}\cdot 2_{1}

(*{\cdot }2{:}2{\cdot }2{:}2)

({\bar {*}}{\cdot }{\bar {*}}{\cdot })

,

[{\times _{0}}{\times _{0}}]

27 Pcc2 P c c 2

\Gamma _{o}C_{2v}^{3}

5h

(c:a:b):{\tilde {c}}\cdot 2

(*{:}2{:}2{:}2{:}2)

({\bar {*}}_{0}{\bar {*}}_{0})

28 Pma2 P m a 2

\Gamma _{o}C_{2v}^{4}

6h

(c:a:b):{\tilde {a}}\cdot 2

(2_{0}2_{0}{*}{\cdot })

[{*}_{0}{:}{*}_{0}{:}]

,

(*{\cdot }{*}_{0})

29 Pca2₁ P c a 2₁

\Gamma _{o}C_{2v}^{5}

11a

(c:a:b):{\tilde {a}}\cdot 2_{1}

(2_{1}2_{1}{*}{:})

({\bar {*}}{:}{\bar {*}}{:})

30 Pnc2 P n c 2

\Gamma _{o}C_{2v}^{6}

7h

(c:a:b):{\tilde {c}}\odot 2

(2_{0}2_{0}{*}{:})

({\bar {*}}_{1}{\bar {*}}_{1})

,

({*}_{0}{\times }_{0})

31 Pmn2₁ P m n 2₁

\Gamma _{o}C_{2v}^{7}

10a

(c:a:b):{\widetilde {ac}}\cdot 2_{1}

(2_{1}2_{1}{*}{\cdot })

(*{\cdot }{\bar {\times }})

,

[{\times }_{0}{\times }_{1}]

32 Pba2 P b a 2

\Gamma _{o}C_{2v}^{8}

9h

(c:a:b):{\tilde {a}}\odot 2

(2_{0}2_{0}{\times }_{0})

(*{:}{*}_{0})

33 Pna2₁ P n a 2₁

\Gamma _{o}C_{2v}^{9}

12a

(c:a:b):{\tilde {a}}\odot 2_{1}

(2_{1}2_{1}{\times })

(*{:}{\times })

,

({\times }{\times }_{1})

34 Pnn2 P n n 2

\Gamma _{o}C_{2v}^{10}

8h

(c:a:b):{\widetilde {ac}}\odot 2

(2_{0}2_{0}{\times }_{1})

(*_{0}{\times }_{1})

35 Cmm2 C m m 2

\Gamma _{o}^{b}C_{2v}^{11}

14s

\left({\tfrac {a+b}{2}}:c:a:b\right):m\cdot 2

(2_{0}{*}{\cdot }2{\cdot }2)

[*_{0}{\cdot }{*}_{0}{:}]

36 Cmc2₁ C m c 2₁

\Gamma _{o}^{b}C_{2v}^{12}

13a

\left({\tfrac {a+b}{2}}:c:a:b\right):{\tilde {c}}\cdot 2_{1}

(2_{1}{*}{\cdot }2{:}2)

({\bar {*}}{\cdot }{\bar {*}}{:})

,

[{\times }_{1}{\times }_{1}]

37 Ccc2 C c c 2

\Gamma _{o}^{b}C_{2v}^{13}

10h

\left({\tfrac {a+b}{2}}:c:a:b\right):{\tilde {c}}\cdot 2

(2_{0}{*}{:}2{:}2)

({\bar {*}}_{0}{\bar {*}}_{1})

38 Amm2 A m m 2

\Gamma _{o}^{b}C_{2v}^{14}

15s

\left({\tfrac {b+c}{2}}/c:a:b\right):m\cdot 2

(*{\cdot }2{\cdot }2{\cdot }2{:}2)

[{*}_{1}{\cdot }{*}_{1}{\cdot }]

,

[*{\cdot }{\times }_{0}]

39 Aem2 A b m 2

\Gamma _{o}^{b}C_{2v}^{15}

11h

\left({\tfrac {b+c}{2}}/c:a:b\right):m\cdot 2_{1}

(*{\cdot }2{:}2{:}2{:}2)

[{*}_{1}{:}{*}_{1}{:}]

,

({\bar {*}}{\cdot }{\bar {*}}_{0})

40 Ama2 A m a 2

\Gamma _{o}^{b}C_{2v}^{16}

12h

\left({\tfrac {b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2

(2_{0}2_{1}{*}{\cdot })

(*{\cdot }{*}_{1})

,

[*{:}{\times }_{1}]

41 Aea2 A b a 2

\Gamma _{o}^{b}C_{2v}^{17}

13h

\left({\tfrac {b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2_{1}

(2_{0}2_{1}{*}{:})

(*{:}{*}_{1})

,

({\bar {*}}{:}{\bar {*}}_{1})

42 Fmm2 F m m 2

\Gamma _{o}^{f}C_{2v}^{18}

17s

\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):m\cdot 2

(*{\cdot }2{\cdot }2{:}2{:}2)

[{*}_{1}{\cdot }{*}_{1}{:}]

43 Fdd2 F d d 2

\Gamma _{o}^{f}C_{2v}^{19}

16h

\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):{\tfrac {1}{2}}{\widetilde {ac}}\odot 2

(2_{0}2_{1}{\times })

({*}_{1}{\times })

44 Imm2 I m m 2

\Gamma _{o}^{v}C_{2v}^{20}

16s

\left({\tfrac {a+b+c}{2}}/c:a:b\right):m\cdot 2

(2_{1}{*}{\cdot }2{\cdot }2)

[*{\cdot }{\times }_{1}]

45 Iba2 I b a 2

\Gamma _{o}^{v}C_{2v}^{21}

15h

\left({\tfrac {a+b+c}{2}}/c:a:b\right):{\tilde {c}}\cdot 2

(2_{1}{*}{:}2{:}2)

({\bar {*}}{:}{\bar {*}}_{0})

46 Ima2 I m a 2

\Gamma _{o}^{v}C_{2v}^{22}

14h

\left({\tfrac {a+b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2

(2_{0}{*}{\cdot }2{:}2)

({\bar {*}}{\cdot }{\bar {*}}_{1})

,

[*{:}{\times }_{0}]

47

{\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}

*222

Pmmm P 2/m 2/m 2/m

\Gamma _{o}D_{2h}^{1}

18s

\left(c:a:b\right)\cdot m:2\cdot m

[*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]

48 Pnnn P 2/n 2/n 2/n

\Gamma _{o}D_{2h}^{2}

19h

\left(c:a:b\right)\cdot {\widetilde {ab}}:2\odot {\widetilde {ac}}

(2{\bar {*}}_{1}2_{0}2_{0})

49 Pccm P 2/c 2/c 2/m

\Gamma _{o}D_{2h}^{3}

17h

\left(c:a:b\right)\cdot m:2\cdot {\tilde {c}}

[*{:}2{:}2{:}2{:}2]

(*2_{0}2_{0}2{\cdot }2)

50 Pban P 2/b 2/a 2/n

\Gamma _{o}D_{2h}^{4}

18h

\left(c:a:b\right)\cdot {\widetilde {ab}}:2\odot {\tilde {a}}

(2{\bar {*}}_{0}2_{0}2_{0})

(*2_{0}2_{0}2{:}2)

51 Pmma P 2₁/m 2/m 2/a

\Gamma _{o}D_{2h}^{5}

14a

\left(c:a:b\right)\cdot {\tilde {a}}:2\cdot m

[2_{0}2_{0}{*}{\cdot }]

[*{\cdot }2{:}2{\cdot }2{:}2]

,

[*2{\cdot }2{\cdot }2{\cdot }2]

52 Pnna P 2/n 2₁/n 2/a

\Gamma _{o}D_{2h}^{6}

17a

\left(c:a:b\right)\cdot {\tilde {a}}:2\odot {\widetilde {ac}}

(2_{0}2{\bar {*}}_{1})

(2_{0}{*}2{:}2)

,

(2{\bar {*}}2_{1}2_{1})

53 Pmna P 2/m 2/n 2₁/a

\Gamma _{o}D_{2h}^{7}

15a

\left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\cdot {\widetilde {ac}}

[2_{0}2_{0}{*}{:}]

(*2_{1}2_{1}2{\cdot }2)

,

(2_{0}{*}2{\cdot }2)

54 Pcca P 2₁/c 2/c 2/a

\Gamma _{o}D_{2h}^{8}

16a

\left(c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}

(2_{0}2{\bar {*}}_{0})

(*2{:}2{:}2{:}2)

,

(*2_{1}2_{1}2{:}2)

55 Pbam P 2₁/b 2₁/a 2/m

\Gamma _{o}D_{2h}^{9}

22a

\left(c:a:b\right)\cdot m:2\odot {\tilde {a}}

[2_{0}2_{0}{\times }_{0}]

(*2{\cdot }2{:}2{\cdot }2)

56 Pccn P 2₁/c 2₁/c 2/n

\Gamma _{o}D_{2h}^{10}

27a

\left(c:a:b\right)\cdot {\widetilde {ab}}:2\cdot {\tilde {c}}

(2{\bar {*}}{:}2{:}2)

(2_{1}2{\bar {*}}_{0})

57 Pbcm P 2/b 2₁/c 2₁/m

\Gamma _{o}D_{2h}^{11}

23a

\left(c:a:b\right)\cdot m:2_{1}\odot {\tilde {c}}

(2_{0}2{\bar {*}}{\cdot })

(*2{:}2{\cdot }2{:}2)

,

[2_{1}2_{1}{*}{:}]

58 Pnnm P 2₁/n 2₁/n 2/m

\Gamma _{o}D_{2h}^{12}

25a

\left(c:a:b\right)\cdot m:2\odot {\widetilde {ac}}

[2_{0}2_{0}{\times }_{1}]

(2_{1}{*}2{\cdot }2)

59 Pmmn P 2₁/m 2₁/m 2/n

\Gamma _{o}D_{2h}^{13}

24a

\left(c:a:b\right)\cdot {\widetilde {ab}}:2\cdot m

(2{\bar {*}}{\cdot }2{\cdot }2)

[2_{1}2_{1}{*}{\cdot }]

60 Pbcn P 2₁/b 2/c 2₁/n

\Gamma _{o}D_{2h}^{14}

26a

\left(c:a:b\right)\cdot {\widetilde {ab}}:2_{1}\odot {\tilde {c}}

(2_{0}2{\bar {*}}{:})

(2_{1}{*}2{:}2)

,

(2_{1}2{\bar {*}}_{1})

61 Pbca P 2₁/b 2₁/c 2₁/a

\Gamma _{o}D_{2h}^{15}

29a

\left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\odot {\tilde {c}}

(2_{1}2{\bar {*}}{:})

62 Pnma P 2₁/n 2₁/m 2₁/a

\Gamma _{o}D_{2h}^{16}

28a

\left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\odot m

(2_{1}2{\bar {*}}{\cdot })

(2{\bar {*}}{\cdot }2{:}2)

,

[2_{1}2_{1}{\times }]

63 Cmcm C 2/m 2/c 2₁/m

\Gamma _{o}^{b}D_{2h}^{17}

18a

\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2_{1}\cdot {\tilde {c}}

[2_{0}2_{1}{*}{\cdot }]

(*2{\cdot }2{\cdot }2{:}2)

,

[2_{1}{*}{\cdot }2{:}2]

64 Cmce C 2/m 2/c 2₁/a

\Gamma _{o}^{b}D_{2h}^{18}

19a

\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2_{1}\cdot {\tilde {c}}

[2_{0}2_{1}{*}{:}]

(*2{\cdot }2{:}2{:}2)

,

(*2_{1}2{\cdot }2{:}2)

65 Cmmm C 2/m 2/m 2/m

\Gamma _{o}^{b}D_{2h}^{19}

19s

\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot m

[2_{0}{*}{\cdot }2{\cdot }2]

[*{\cdot }2{\cdot }2{\cdot }2{:}2]

66 Cccm C 2/c 2/c 2/m

\Gamma _{o}^{b}D_{2h}^{20}

20h

\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot {\tilde {c}}

[2_{0}{*}{:}2{:}2]

(*2_{0}2_{1}2{\cdot }2)

67 Cmme C 2/m 2/m 2/e

\Gamma _{o}^{b}D_{2h}^{21}

21h

\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2\cdot m

(*2_{0}2{\cdot }2{\cdot }2)

[*{\cdot }2{:}2{:}2{:}2]

68 Ccce C 2/c 2/c 2/e

\Gamma _{o}^{b}D_{2h}^{22}

22h

\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}

(*2_{0}2{:}2{:}2)

(*2_{0}2_{1}2{:}2)

69 Fmmm F 2/m 2/m 2/m

\Gamma _{o}^{f}D_{2h}^{23}

21s

\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot m

[*{\cdot }2{\cdot }2{:}2{:}2]

70 Fddd F 2/d 2/d 2/d

\Gamma _{o}^{f}D_{2h}^{24}

24h

\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tfrac {1}{2}}{\widetilde {ab}}:2\odot {\tfrac {1}{2}}{\widetilde {ac}}

(2{\bar {*}}2_{0}2_{1})

71 Immm I 2/m 2/m 2/m

\Gamma _{o}^{v}D_{2h}^{25}

20s

\left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot m:2\cdot m

[2_{1}{*}{\cdot }2{\cdot }2]

72 Ibam I 2/b 2/a 2/m

\Gamma _{o}^{v}D_{2h}^{26}

23h

\left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot m:2\cdot {\tilde {c}}

[2_{1}{*}{:}2{:}2]

(*2_{0}2{\cdot }2{:}2)

73 Ibca I 2/b 2/c 2/a

\Gamma _{o}^{v}D_{2h}^{27}

21a

\left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}

(*2_{1}2{:}2{:}2)

74 Imma I 2/m 2/m 2/a

\Gamma _{o}^{v}D_{2h}^{28}

20a

\left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot {\tilde {a}}:2\cdot m

(*2_{1}2{\cdot }2{\cdot }2)

[2_{0}{*}{\cdot }2{:}2]

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