Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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. #11720924 | C2 | semidirect |
| 5. #11720539 | C2 | semidirect |
| 6. C3×Dic9⋊C8 | C2 | semidirect |
| 7. #11720298 | C2 | semidirect |
| 37. Dic9⋊C8 | D3 | semidirect |
| 95. C3×Dic9 | SD16 | semidirect |
| 209. Dic9 | #204 | semidirect |
| 217. C3×C9 | #461 | semidirect |
| 309. C9 | #4841 | semidirect |
| 349. C3 | #10588842 | 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 |
| #11720924 | 2 |
| C2×#88424 | 2 |
| #11720539 | 2 |
| C3×Dic9⋊C8 | 2 |
| #11720298 | 2 |
| #10590752 | 3 |
| #10588842 | 3 |