Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1569 conjugacy classes of subgroups; only the 300 normal subgroups are shown.
This group has 1569 conjugacy classes of subgroups — too many to draw. Only its 300 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 |
| 3. #10592631 | C2 | semidirect |
| 4. #10591381 | C2 | semidirect |
| 5. #10591323 | C2 | semidirect |
| 6. #10591230 | C2 | semidirect |
| 18. #63914 | C4 | semidirect |
| 23. C2×C4×D12 | D3 | semidirect |
| 39. C2×C3×D12 | C2×C4 | semidirect |
| 43. C2×#625 | C2×C4 | semidirect |
| 44. C32×C42 | D4 | semidirect |
| 46. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 124. C2×D12 | C4×D3 | semidirect |
| 130. C3×C42 | #67 | semidirect |
| 232. C42 | #625 | semidirect |
| 263. C32 | #2328 | semidirect |
| 310. C3 | #82329 | 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 |
| C2×#63914 | 2 |
| #10592631 | 2 |
| #10591381 | 2 |
| #10591323 | 2 |
| #10591230 | 2 |
| #82329 | 3 |