Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
392 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11721706 | C2 | semidirect |
| 3. C3×C4⋊(C9⋊C8) | C2 | semidirect |
| 5. #11720264 | C2 | semidirect |
| 27. C4⋊(C9⋊C8) | D3 | semidirect |
| 36. C9×D12 | Q8 | semidirect |
| 169. C3×C9 | #476 | semidirect |
| 190. D12 | Dic18 | semidirect |
| 245. C9 | #4842 | semidirect |
| 279. C3 | #10588691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721706 | 2 |
| C4×C9×D12 | 2 |
| C3×C4⋊(C9⋊C8) | 2 |
| #11720295 | 2 |
| #11720264 | 2 |
| #10590268 | 3 |
| #10588691 | 3 |