Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
366 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 13. C3×Dic36 | C4 | semidirect |
| 55. Dic36 | Dic3 | direct (N × H) |
| 61. C9×Dic3 | Q16 | semidirect |
| 140. C3×C9 | C4×Q16 | semidirect |
| 196. Dic3 | Dic36 | direct (N × H) |
| 199. C9 | Dic3×Q16 | semidirect |
| 226. C3 | C4×Dic36 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic36 | 2 |
| Dic3×Dic18 | 2 |
| #11720541 | 2 |
| C8×C9×Dic3 | 2 |
| #11720276 | 2 |
| Dic3×Dic12 | 3 |
| C4×Dic36 | 3 |