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 |
|---|---|---|
| 191. C3×C9 | #491 | semidirect |
| 269. C9 | #4797 | semidirect |
| 302. C3 | #10588762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#944 | 2 |
| #11720927 | 2 |
| #11720582 | 2 |
| C3×#63395 | 2 |
| #11720298 | 2 |
| #11720297 | 2 |
| #11720258 | 2 |
| #10591613 | 3 |
| #10588762 | 3 |