Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
405 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 405 conjugacy classes of subgroups — too many to draw. Only its 114 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. C32×#494 | C2 | semidirect |
| 4. C3×#4547 | C2 | semidirect |
| 5. C3×#4458 | C2 | semidirect |
| 7. #71305 | C3 | direct (N × H) |
| 20. C3×#494 | D3 | semidirect |
| 21. C3×#494 | C2×C3 | semidirect |
| 28. #4547 | C2×C3 | semidirect |
| 29. #4458 | C2×C3 | semidirect |
| 81. C3×D12 | Q16 | semidirect |
| 88. #494 | C3×D3 | semidirect |
| 180. D12 | C3×Q16 | semidirect |
| 241. C32 | #1669 | semidirect |
| 281. C3 | #71305 | direct (N × H) |
| 282. C3 | C3×#1669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#494 | 2 |
| C3×#5087 | 2 |
| C3×C8×D12 | 2 |
| C3×#4547 | 2 |
| C3×#4458 | 2 |
| C3×#1669 | 3 |
| #71305 | 3 |