Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1198 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 1198 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 |
|---|---|---|
| 4. #10596543 | C2 | direct (N × H) |
| 5. C2×C4⋊PSU(3,𝔽2) | C2 | semidirect |
| 6. C2×#64243 | C2 | semidirect |
| 20. C4⋊PSU(3,𝔽2) | C22 | semidirect |
| 21. #64243 | C22 | semidirect |
| 30. C22×C32×C4 | Q8 | semidirect |
| 31. C22×C3⋊Dic3 | Q8 | semidirect |
| 32. C2×C4×C3⋊D3 | Q8 | semidirect |
| 33. C2×C4×C3⋊D3 | Q8 | semidirect |
| 61. C2×C32×C4 | C2×Q8 | semidirect |
| 63. C2×C3⋊Dic3 | C2×Q8 | semidirect |
| 65. C4×C3⋊D3 | C2×Q8 | semidirect |
| 127. C2×C32 | #544 | semidirect |
| 130. C3⋊D3 | #544 | semidirect |
| 146. C22×C4 | PSU(3,𝔽2) | semidirect |
| 168. C32 | C2×#544 | semidirect |
| 190. C2×C4 | C2×PSU(3,𝔽2) | semidirect |
| 221. C2 | #10596543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64286 | 2 |
| C22×C4⋊#157 | 2 |
| C2×C22⋊PSU(3,𝔽2) | 2 |
| #10596543 | 2 |
| C2×C4⋊PSU(3,𝔽2) | 2 |
| C2×#64243 | 2 |
| C2×#544 | 9 |