Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
338 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 2. #11720935 | C2 | semidirect |
| 5. #11720276 | C2 | semidirect |
| 6. C3⋊C8×Dic9 | C2 | semidirect |
| 7. #11720268 | C2 | semidirect |
| 200. C3×C9 | #488 | semidirect |
| 287. C9 | #5056 | semidirect |
| 325. C3 | #10588448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63498 | 2 |
| #11720935 | 2 |
| #11720576 | 2 |
| C9×#832 | 2 |
| #11720276 | 2 |
| C3⋊C8×Dic9 | 2 |
| #11720268 | 2 |
| #10591478 | 3 |
| #10588448 | 3 |