Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
330 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 81 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×#63452 | C2 | semidirect |
| 3. #11720527 | C2 | semidirect |
| 6. #11720277 | C2 | semidirect |
| 7. C3⋊C8×Dic9 | C2 | semidirect |
| 29. #63452 | D3 | semidirect |
| 198. C3×C9 | #488 | semidirect |
| 282. C9 | #5068 | semidirect |
| 319. C3 | #10588448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63452 | 2 |
| #11720964 | 2 |
| #11720527 | 2 |
| C9×#809 | 2 |
| #11720294 | 2 |
| #11720277 | 2 |
| C3⋊C8×Dic9 | 2 |
| #10590533 | 3 |
| #10588448 | 3 |