Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
336 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 194. C3×C9 | #487 | semidirect |
| 274. C9 | #4681 | semidirect |
| 308. C3 | #10588472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720969 | 2 |
| #11720924 | 2 |
| #11720539 | 2 |
| C9×#816 | 2 |
| C3×C8×Dic9 | 2 |
| #11720298 | 2 |
| #11720269 | 2 |
| #10590890 | 3 |
| #10588472 | 3 |