Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 4. #11720275 | C2 | semidirect |
| 5. #11720273 | C2 | semidirect |
| 6. #11720273 | C2 | semidirect |
| 7. #11720271 | C2 | semidirect |
| 215. C3×C9 | #433 | semidirect |
| 309. C9 | #4720 | semidirect |
| 347. C3 | #10588400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721815 | 2 |
| C9×#830 | 2 |
| C3×#63389 | 2 |
| #11720275 | 2 |
| #11720273 | 2 |
| #11720271 | 2 |
| #10591062 | 3 |
| #10588400 | 3 |