Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 3. C3×C9×#106 | C2 | semidirect |
| 5. #11720539 | C2 | semidirect |
| 6. #11720527 | C2 | semidirect |
| 7. #11720525 | C2 | semidirect |
| 30. C9×#106 | D3 | semidirect |
| 87. C3×#106 | D9 | semidirect |
| 175. #106 | C3⋊D9 | semidirect |
| 179. C3×C9 | #485 | semidirect |
| 248. C9 | #4868 | semidirect |
| 281. C3 | #10588548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721753 | 2 |
| #11721748 | 2 |
| C3×C9×#106 | 2 |
| #11720542 | 2 |
| #11720539 | 2 |
| #11720527 | 2 |
| #11720525 | 2 |
| #10592567 | 3 |
| #10588548 | 3 |