Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 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. #11721707 | C2 | semidirect |
| 3. C3×#63362 | C2 | semidirect |
| 4. #11720295 | C2 | semidirect |
| 21. #63362 | D3 | semidirect |
| 117. C3×C9 | #490 | semidirect |
| 167. C9 | #4713 | semidirect |
| 190. C3 | #10588751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721707 | 2 |
| C9×#874 | 2 |
| C3×#63362 | 2 |
| #11720295 | 2 |
| #10590275 | 3 |
| #10588751 | 3 |