Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 185. C3×C9 | #479 | semidirect |
| 259. C9 | #5063 | semidirect |
| 290. C3 | #10588537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63452 | 2 |
| #11720913 | 2 |
| #11720527 | 2 |
| C9×#808 | 2 |
| #11720277 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #11720263 | 2 |
| #10590490 | 3 |
| #10588537 | 3 |