Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
306 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 183. C3×C9 | #479 | semidirect |
| 255. C9 | #4796 | semidirect |
| 286. C3 | #10588511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720927 | 2 |
| Dic3×Dic18 | 2 |
| #11720541 | 2 |
| C9×Dic3⋊C8 | 2 |
| C3×#63376 | 2 |
| #11720278 | 2 |
| #11720276 | 2 |
| #10590811 | 3 |
| #10588511 | 3 |