Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
294 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 129. C3×C9 | #499 | semidirect |
| 183. C9 | #4683 | semidirect |
| 208. C3 | #10588558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720935 | 2 |
| #11720541 | 2 |
| C9×#818 | 2 |
| C3×C8×Dic9 | 2 |
| #11720264 | 2 |
| #10590873 | 3 |
| #10588558 | 3 |