Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
294 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 122. C3×C9 | #499 | semidirect |
| 169. C9 | #4858 | semidirect |
| 189. C3 | #10588363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720927 | 2 |
| #11720540 | 2 |
| C8×C9×Dic3 | 2 |
| C3×#63377 | 2 |
| #11720279 | 2 |
| #10590871 | 3 |
| #10588363 | 3 |