Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
446 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 446 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. #11721025 | C2 | semidirect |
| 3. C8×C3⋊Dic9 | C2 | semidirect |
| 4. C3×#63378 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 14. C9×D24 | C4 | semidirect |
| 24. #63378 | D3 | semidirect |
| 33. C9×D12 | C2×C4 | semidirect |
| 35. C3×C8×C9 | C2×C4 | semidirect |
| 65. C3⋊Dic9 | D8 | semidirect |
| 100. C8×C9 | C4×D3 | semidirect |
| 126. D24 | Dic9 | semidirect |
| 155. C3×C9 | C4×D8 | semidirect |
| 173. D12 | C2×Dic9 | semidirect |
| 176. C3×C8 | C2×Dic9 | semidirect |
| 225. C9 | #4872 | semidirect |
| 235. C8 | D3×Dic9 | semidirect |
| 257. 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 |
| #11721025 | 2 |
| C8×C3⋊Dic9 | 2 |
| C3×#63378 | 2 |
| #11720294 | 2 |
| #10590777 | 3 |
| D8×Dic9 | 3 |