Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
390 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 10. #88521 | C4 | semidirect |
| 62. C9×Dic3 | Q16 | semidirect |
| 144. C3×C9 | C4×Q16 | semidirect |
| 202. Dic3 | Dic36 | semidirect |
| 205. C9 | #4873 | semidirect |
| 232. C3 | C4×Dic36 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| #11720912 | 2 |
| C8×C9×Dic3 | 2 |
| C3×#63378 | 2 |
| #11720277 | 2 |
| #10590807 | 3 |
| C4×Dic36 | 3 |