Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
480 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 3. #11720582 | C2 | semidirect |
| 4. #11720582 | C2 | semidirect |
| 6. #11720526 | C2 | semidirect |
| 7. #11720525 | C2 | semidirect |
| 179. C3×C9 | #485 | semidirect |
| 248. C9 | #5045 | semidirect |
| 281. C3 | #10588725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C22⋊Q8 | 2 |
| #11721815 | 2 |
| #11720582 | 2 |
| #11720571 | 2 |
| #11720526 | 2 |
| #11720525 | 2 |
| #10592744 | 3 |
| #10588725 | 3 |