Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1057 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 1057 conjugacy classes of subgroups — too many to draw. Only its 160 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. #10596269 | C2 | semidirect |
| 3. C2×C3×#833 | C2 | semidirect |
| 4. #10591086 | C2 | semidirect |
| 5. #10589162 | C2 | semidirect |
| 15. C3×#940 | C4 | semidirect |
| 26. C2×#833 | D3 | semidirect |
| 45. C2×C3×D12 | C2×C4 | semidirect |
| 48. C4⋊(C3⋊Dic3) | D4 | semidirect |
| 51. C3×C4×Dic3 | C2×C4 | semidirect |
| 71. #940 | Dic3 | semidirect |
| 148. C2×D12 | C2×Dic3 | semidirect |
| 167. C4×Dic3 | C2×Dic3 | semidirect |
| 331. C32 | #1887 | semidirect |
| 389. C3 | #70070 | semidirect |
| 390. C3 | #71763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596269 | 2 |
| C2×C3×#940 | 2 |
| C2×C3×#833 | 2 |
| #10591086 | 2 |
| #10589162 | 2 |
| #71763 | 3 |
| #70070 | 3 |