Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
357 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 1. C2×C32×Q32 | C2 | semidirect |
| 3. C3×Dic3×Q16 | C2 | semidirect |
| 5. C3×#4564 | C2 | semidirect |
| 7. C3×Dic3⋊C16 | C2 | semidirect |
| 9. #71498 | C3 | direct (N × H) |
| 24. C2×C3×Q32 | D3 | semidirect |
| 25. C2×C3×Q32 | C2×C3 | semidirect |
| 30. Dic3×Q16 | C2×C3 | semidirect |
| 35. #4564 | C2×C3 | semidirect |
| 37. Dic3⋊C16 | C2×C3 | semidirect |
| 105. C2×Q32 | C3×D3 | semidirect |
| 276. C32 | #2211 | semidirect |
| 316. C3 | #71498 | direct (N × H) |
| 317. C3 | C3×#2211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q32 | 2 |
| C3×#5191 | 2 |
| C3×Dic3×Q16 | 2 |
| C2×C3×#828 | 2 |
| C3×#4564 | 2 |
| C3×#4509 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#2211 | 3 |
| #71498 | 3 |