Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
402 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 3. Dic6×Dic9 | C2 | semidirect |
| 4. #11720540 | C2 | semidirect |
| 5. C3×C8×Dic9 | C2 | semidirect |
| 6. #11720298 | C2 | semidirect |
| 18. C9×#204 | C4 | semidirect |
| 36. C8×Dic9 | D3 | semidirect |
| 47. C9×Dic6 | C2×C4 | semidirect |
| 49. C3×C8×C9 | C2×C4 | semidirect |
| 90. C3×Dic9 | SD16 | semidirect |
| 136. C8×C9 | C4×D3 | semidirect |
| 169. #204 | Dic9 | direct (N × H) |
| 196. Dic9 | #204 | direct (N × H) |
| 204. C3×C9 | C4×SD16 | semidirect |
| 231. Dic6 | C2×Dic9 | semidirect |
| 234. C3×C8 | C2×Dic9 | semidirect |
| 289. C9 | C4×#204 | semidirect |
| 303. C8 | D3×Dic9 | semidirect |
| 327. C3 | SD16×Dic9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#204 | 2 |
| D12×Dic9 | 2 |
| Dic6×Dic9 | 2 |
| #11720540 | 2 |
| C3×C8×Dic9 | 2 |
| #11720298 | 2 |
| #11720295 | 2 |
| Dic3×#204 | 3 |
| SD16×Dic9 | 3 |