Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
471 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 471 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#92344 |
| commutator, cosocle | C2×#6908 | C22 |
| Frattini | C2×C32 | C2×C3⋊(C3⋊D3) |
| Fitting | C4×#6908 | C2 |
| socle | C2×C3 | C2×C3⋊#272 |
| hypercenter | C4 | #92344 |
| hypocenter | #6908 | D4 |
| LCS | G ▷ C2×#6908 ▷ #6908 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#92344 | C2 | semidirect |
| 2. C4×#6908 | C2 | semidirect |
| 13. C4×#737 | D3 | semidirect |
| 14. C32×C4×C9 | D3 | semidirect |
| 19. C4×#733 | D3 | semidirect |
| 20. C4×#732 | D3 | semidirect |
| 21. C4×#731 | D3 | semidirect |
| 22. C4×AΣL(1,𝔽27) | D3 | semidirect |
| 23. #6908 | D4 | semidirect |
| 62. #737 | D12 | semidirect |
| 63. C32×C9 | D12 | semidirect |
| 64. #733 | D12 | semidirect |
| 65. #732 | D12 | semidirect |
| 66. #731 | D12 | semidirect |
| 67. AΣL(1,𝔽27) | D12 | semidirect |
| 169. C4 | #92344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92344 | 2 |
| C4×#6908 | 2 |
| C4⋊#4207 | 3 |
| C3×C4⋊(C3⋊D9) | 3 |
| C4⋊(#733⋊C2) | 3 |
| C4⋊#4185 | 3 |
| C4⋊#4184 | 3 |
| C4⋊#4183 | 3 |