Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
438 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. D12×Dic9 | C2 | semidirect |
| 3. #11720541 | C2 | semidirect |
| 4. C3×C8×Dic9 | C2 | semidirect |
| 5. #11720295 | C2 | semidirect |
| 14. C9×D24 | C4 | semidirect |
| 26. C8×Dic9 | D3 | semidirect |
| 33. C9×D12 | C2×C4 | semidirect |
| 35. C3×C8×C9 | C2×C4 | semidirect |
| 65. C3×Dic9 | D8 | semidirect |
| 98. C8×C9 | C4×D3 | semidirect |
| 122. D24 | Dic9 | direct (N × H) |
| 144. Dic9 | D24 | direct (N × H) |
| 150. C3×C9 | C4×D8 | semidirect |
| 167. D12 | C2×Dic9 | semidirect |
| 171. C3×C8 | C2×Dic9 | semidirect |
| 217. C9 | C4×D24 | semidirect |
| 227. C8 | D3×Dic9 | semidirect |
| 249. C3 | D8×Dic9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D24 | 2 |
| D12×Dic9 | 2 |
| #11720541 | 2 |
| C3×C8×Dic9 | 2 |
| #11720295 | 2 |
| Dic3×D24 | 3 |
| D8×Dic9 | 3 |