Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
889 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 889 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 |
|---|---|---|
| 4. #10591100 | C2 | semidirect |
| 5. #10589162 | C2 | semidirect |
| 15. C3×#936 | C4 | semidirect |
| 43. C2×C3×Dic6 | C2×C4 | semidirect |
| 50. C3×C4×Dic3 | C2×C4 | semidirect |
| 70. #936 | Dic3 | semidirect |
| 141. C2×Dic6 | C2×Dic3 | semidirect |
| 162. C4×Dic3 | C2×Dic3 | semidirect |
| 311. C32 | #1885 | semidirect |
| 362. C3 | #70069 | semidirect |
| 363. C3 | #71723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596269 | 2 |
| C2×C3×#936 | 2 |
| C2×C3×#833 | 2 |
| #10591100 | 2 |
| #10589162 | 2 |
| #71723 | 3 |
| #70069 | 3 |