Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
452 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 1. C3×D4×Dic9 | C2 | semidirect |
| 3. D12×Dic9 | C2 | semidirect |
| 4. #11720576 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 6. #11720279 | C2 | semidirect |
| 7. C3⋊C8×Dic9 | C2 | semidirect |
| 17. C9×#213 | C4 | semidirect |
| 31. D4×Dic9 | D3 | semidirect |
| 40. C3×D4×C9 | C2×C4 | semidirect |
| 48. C9×D12 | C2×C4 | semidirect |
| 51. C9×C3⋊C8 | C2×C4 | semidirect |
| 93. C3×Dic9 | D8 | semidirect |
| 132. D4×C9 | C4×D3 | semidirect |
| 167. #213 | Dic9 | direct (N × H) |
| 210. Dic9 | #213 | direct (N × H) |
| 218. C3×C9 | C4×D8 | semidirect |
| 230. C3×D4 | C2×Dic9 | semidirect |
| 248. D12 | C2×Dic9 | semidirect |
| 254. C3⋊C8 | C2×Dic9 | semidirect |
| 316. C9 | C4×#213 | semidirect |
| 322. D4 | D3×Dic9 | semidirect |
| 360. C3 | D8×Dic9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×Dic9 | 2 |
| C2×C9×#213 | 2 |
| D12×Dic9 | 2 |
| #11720576 | 2 |
| #11720294 | 2 |
| #11720279 | 2 |
| C3⋊C8×Dic9 | 2 |
| Dic3×#213 | 3 |
| D8×Dic9 | 3 |