Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
530 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 151 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×#117 | C2 | semidirect |
| 3. #11720571 | C2 | semidirect |
| 4. #11720528 | C2 | semidirect |
| 5. #11720528 | C2 | semidirect |
| 6. #11720526 | C2 | semidirect |
| 7. #11720525 | C2 | semidirect |
| 28. C9×#117 | D3 | semidirect |
| 86. C3×#117 | D9 | semidirect |
| 183. #117 | C3⋊D9 | semidirect |
| 189. C3×C9 | #482 | semidirect |
| 266. C9 | #5003 | semidirect |
| 304. C3 | #10588684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#117 | 2 |
| #11721819 | 2 |
| #11720571 | 2 |
| #11720528 | 2 |
| #11720526 | 2 |
| #11720525 | 2 |
| #10592702 | 3 |
| #10588684 | 3 |