Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
730 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 171 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. C3×C9×2−1+4 | C2 | semidirect |
| 2. #11721867 | C2 | semidirect |
| 3. #11721857 | C2 | semidirect |
| 4. #11720585 | C2 | semidirect |
| 5. #11720581 | C2 | semidirect |
| 22. C9×2−1+4 | D3 | semidirect |
| 75. C3×2−1+4 | D9 | semidirect |
| 156. 2−1+4 | C3⋊D9 | semidirect |
| 161. C3×C9 | #454 | semidirect |
| 226. C9 | #5245 | semidirect |
| 257. C3 | #10588926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×2−1+4 | 2 |
| #11721867 | 2 |
| #11721857 | 2 |
| #11720585 | 2 |
| #11720581 | 2 |
| #10592944 | 3 |
| #10588926 | 3 |