Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
422 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×C9×#204 | C2 | semidirect |
| 2. D12×Dic9 | C2 | semidirect |
| 3. #11720953 | C2 | semidirect |
| 5. #11720543 | C2 | semidirect |
| 6. C3×Dic9⋊C8 | C2 | semidirect |
| 7. #11720298 | C2 | semidirect |
| 37. Dic9⋊C8 | D3 | semidirect |
| 103. C2×#204 | D9 | semidirect |
| 226. C3×C9 | #463 | semidirect |
| 327. C9 | #4844 | semidirect |
| 372. C3 | #10588845 | 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 |
| #11720953 | 2 |
| C2×#88422 | 2 |
| #11720543 | 2 |
| C3×Dic9⋊C8 | 2 |
| #11720298 | 2 |
| #10590754 | 3 |
| #10588845 | 3 |