Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
432 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11720540 | C2 | semidirect |
| 4. C3×#63375 | C2 | semidirect |
| 5. #11720295 | C2 | semidirect |
| 14. C9×D24 | C4 | semidirect |
| 26. #63375 | D3 | semidirect |
| 32. C9×D12 | C2×C4 | semidirect |
| 34. C3×C8×C9 | C2×C4 | semidirect |
| 94. C8×C9 | C4×D3 | semidirect |
| 117. D24 | Dic9 | semidirect |
| 143. C3×C9 | #442 | semidirect |
| 158. D12 | C2×Dic9 | semidirect |
| 162. C3×C8 | C2×Dic9 | semidirect |
| 203. C9 | #4711 | semidirect |
| 212. C8 | D3×Dic9 | semidirect |
| 230. C3 | #10588832 | 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 |
| #11720540 | 2 |
| C3×#63375 | 2 |
| #11720295 | 2 |
| #10590771 | 3 |
| #10588832 | 3 |