Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
286 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 48 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. #11724364 | C2 | semidirect |
| 3. #11722807 | C2 | semidirect |
| 4. #11722803 | C2 | semidirect |
| 5. C3×#63746 | C2 | semidirect |
| 25. #63746 | D3 | semidirect |
| 35. C4⋊(C3⋊(C3⋊D3)) | Q8 | semidirect |
| 37. C32×D12 | Q8 | semidirect |
| 139. C33 | #474 | semidirect |
| 154. D12 | PSU(3,𝔽2) | semidirect |
| 206. C32 | #4890 | semidirect |
| 247. C3 | #10593558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724364 | 2 |
| #11724259 | 2 |
| #11722807 | 2 |
| #11722803 | 2 |
| C3×#63746 | 2 |
| #11722707 | 2 |
| #11722706 | 2 |
| #10593558 | 3 |
| #4890 | 9 |