Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
849 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 849 conjugacy classes of subgroups — too many to draw. Only its 236 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. C22×C3×Dic12 | C2 | semidirect |
| 3. C22×C3⋊(C3⋊C16) | C2 | semidirect |
| 4. C2×#63547 | C2 | direct (N × H) |
| 11. C2×C3×Dic12 | C22 | semidirect |
| 14. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 15. #63547 | C22 | direct (N × H) |
| 18. C22×Dic12 | D3 | semidirect |
| 35. C3×Dic12 | C23 | semidirect |
| 38. C3⋊(C3⋊C16) | C23 | semidirect |
| 52. C2×Dic12 | C2×D3 | semidirect |
| 102. Dic12 | C22×D3 | semidirect |
| 108. C22×C32 | SD32 | semidirect |
| 153. C2×C32 | C2×SD32 | semidirect |
| 174. C22×C3 | #827 | semidirect |
| 175. C22×C3 | #828 | semidirect |
| 188. C32 | C22×SD32 | semidirect |
| 204. C2×C3 | C2×#827 | semidirect |
| 205. C2×C3 | C2×#828 | semidirect |
| 211. C22 | #63547 | direct (N × H) |
| 217. C3 | C22×#827 | semidirect |
| 218. C3 | C22×#828 | semidirect |
| 220. C2 | C2×#63547 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic12 | 2 |
| C22×C3×D24 | 2 |
| C22×C3⋊(C3⋊C16) | 2 |
| C2×#63547 | 2 |
| C22×#828 | 3 |
| C22×#827 | 3 |