Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
426 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 65. C9×Dic3 | Q16 | semidirect |
| 148. C3×C9 | #494 | semidirect |
| 204. Dic3 | Dic36 | semidirect |
| 207. C9 | #5183 | semidirect |
| 231. C3 | #10588365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| C2×C3×Dic36 | 2 |
| #11720932 | 2 |
| C2×#88418 | 2 |
| C8×C9×Dic3 | 2 |
| #10590896 | 3 |
| #10588365 | 3 |