Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
364 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11720937 | C2 | semidirect |
| 5. #11720277 | C2 | semidirect |
| 6. #11720271 | C2 | semidirect |
| 7. #11720269 | C2 | semidirect |
| 209. C3×C9 | #488 | semidirect |
| 301. C9 | #4768 | semidirect |
| 339. C3 | #10588448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721836 | 2 |
| #11720937 | 2 |
| C9×#832 | 2 |
| C3×#63392 | 2 |
| #11720277 | 2 |
| #11720271 | 2 |
| #11720269 | 2 |
| #10591403 | 3 |
| #10588448 | 3 |