Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1150 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 1150 conjugacy classes of subgroups — too many to draw. Only its 455 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10596547 | C2 | semidirect |
| 3. Q8×PSU(3,𝔽2) | C2 | semidirect |
| 4. #10596545 | C2 | semidirect |
| 5. D4×PSU(3,𝔽2) | C2 | semidirect |
| 6. #10596542 | C2 | semidirect |
| 7. C2×C4×PSU(3,𝔽2) | C2 | semidirect |
| 33. C32×#41 | Q8 | semidirect |
| 34. #3832 | Q8 | semidirect |
| 36. #3830 | Q8 | semidirect |
| 38. #3828 | Q8 | semidirect |
| 62. PSU(3,𝔽2) | #41 | direct (N × H) |
| 63. C32×Q8 | C2×Q8 | semidirect |
| 64. C32×D4 | C2×Q8 | semidirect |
| 65. C2×C32×C4 | C2×Q8 | semidirect |
| 66. #638 | C2×Q8 | semidirect |
| 67. C2×C3⋊Dic3 | C2×Q8 | semidirect |
| 68. C4⋊(C3⋊D3) | C2×Q8 | semidirect |
| 69. C4×C3⋊D3 | C2×Q8 | semidirect |
| 70. C4×C3⋊D3 | C2×Q8 | semidirect |
| 73. #634 | C2×Q8 | semidirect |
| 140. #41 | PSU(3,𝔽2) | direct (N × H) |
| 170. C32 | Q8×#41 | semidirect |
| 176. Q8 | C2×PSU(3,𝔽2) | semidirect |
| 179. D4 | C2×PSU(3,𝔽2) | semidirect |
| 191. C2×C4 | C2×PSU(3,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#157 | 2 |
| #10596547 | 2 |
| Q8×PSU(3,𝔽2) | 2 |
| #10596545 | 2 |
| D4×PSU(3,𝔽2) | 2 |
| #10596542 | 2 |
| C2×C4×PSU(3,𝔽2) | 2 |
| Q8×#41 | 9 |