Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
280 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 65 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. #11720812 | C2 | semidirect |
| 2. #11720507 | C2 | semidirect |
| 3. D3×C9×C16 | C2 | semidirect |
| 4. C3×Dic72 | C2 | semidirect |
| 5. #11720234 | C2 | semidirect |
| 22. Dic72 | D3 | semidirect |
| 66. D3×C16 | D9 | semidirect |
| 120. C3×C9 | #508 | semidirect |
| 166. C9 | #4919 | semidirect |
| 188. C3 | #10588584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720812 | 2 |
| #11720507 | 2 |
| D3×C9×C16 | 2 |
| C3×Dic72 | 2 |
| #11720234 | 2 |
| #10590243 | 3 |
| #10588584 | 3 |