Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
308 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 184. C3×C9 | #479 | semidirect |
| 257. C9 | #4877 | semidirect |
| 288. C3 | #10588476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720937 | 2 |
| #11720911 | 2 |
| #11720537 | 2 |
| C9×#816 | 2 |
| C3×#63378 | 2 |
| #11720297 | 2 |
| #11720265 | 2 |
| #10590821 | 3 |
| #10588476 | 3 |