Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
368 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. #11720537 | C2 | semidirect |
| 4. C3×#63375 | C2 | semidirect |
| 6. #11720274 | C2 | semidirect |
| 7. #11720273 | C2 | semidirect |
| 32. #63375 | D3 | semidirect |
| 203. C3×C9 | #432 | semidirect |
| 290. C9 | #4705 | semidirect |
| 329. C3 | #10588399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D3×Dic9 | 2 |
| #11720537 | 2 |
| C9×(C2×D3)⋊C8 | 2 |
| C3×#63375 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #11720274 | 2 |
| #11720273 | 2 |
| #10590660 | 3 |
| #10588399 | 3 |