Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
404 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 89 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×#63450 | C2 | semidirect |
| 3. #11720528 | C2 | semidirect |
| 4. C9×#809 | C2 | semidirect |
| 5. #11720294 | C2 | semidirect |
| 6. #11720284 | C2 | semidirect |
| 7. C3⋊C8×Dic9 | C2 | semidirect |
| 29. #63450 | D3 | semidirect |
| 105. #809 | D9 | semidirect |
| 216. C3×C9 | #486 | semidirect |
| 315. C9 | #5088 | semidirect |
| 360. C3 | #10588440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63450 | 2 |
| #11721040 | 2 |
| #11720528 | 2 |
| C9×#809 | 2 |
| #11720294 | 2 |
| #11720284 | 2 |
| C3⋊C8×Dic9 | 2 |
| #10590548 | 3 |
| #10588440 | 3 |