Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
920 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 200 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. #11723910 | C2 | semidirect |
| 3. C3×C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. #11722057 | C2 | semidirect |
| 24. C4⋊(C3⋊(C3⋊C8)) | D3 | semidirect |
| 36. C32×D12 | Q8 | semidirect |
| 107. C3×D12 | Dic6 | semidirect |
| 169. C33 | #474 | semidirect |
| 190. D12 | #634 | semidirect |
| 244. C32 | #4846 | semidirect |
| 245. C32 | #5007 | semidirect |
| 279. C3 | #10590272 | semidirect |
| 280. C3 | #10592706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723910 | 2 |
| C32×C4×D12 | 2 |
| C3×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #11722057 | 2 |
| #11722032 | 2 |
| #10592706 | 3 |
| #10590272 | 3 |