Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1769 conjugacy classes of subgroups; only the 378 normal subgroups are shown.
This group has 1769 conjugacy classes of subgroups — too many to draw. Only its 378 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×C3×C4×D12 | C2 | semidirect |
| 2. C32×#376 | C2 | semidirect |
| 3. C3×#4677 | C2 | semidirect |
| 4. C3×#4671 | C2 | semidirect |
| 6. #73418 | C3 | direct (N × H) |
| 15. C2×C4×D12 | C2×C3 | semidirect |
| 19. C3×#376 | D3 | semidirect |
| 20. C3×#376 | C2×C3 | semidirect |
| 21. #4677 | C2×C3 | semidirect |
| 22. #4671 | C2×C3 | semidirect |
| 30. C32×C42 | D4 | semidirect |
| 63. #376 | C3×D3 | semidirect |
| 83. C3×C42 | D12 | semidirect |
| 84. C3×C42 | C3×D4 | semidirect |
| 138. C42 | C3×D12 | semidirect |
| 159. C32 | #2397 | semidirect |
| 187. C3 | #73418 | direct (N × H) |
| 188. C3 | C3×#2397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D12 | 2 |
| C32×#376 | 2 |
| C3×#4677 | 2 |
| C3×#4671 | 2 |
| C3×#2397 | 3 |
| #73418 | 3 |