Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. C3×#63431 | C2 | semidirect |
| 3. #11720516 | C2 | semidirect |
| 4. #11720297 | C2 | semidirect |
| 23. #63431 | D3 | semidirect |
| 156. C3×C9 | #489 | semidirect |
| 225. C9 | #5089 | semidirect |
| 257. C3 | #10588734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#875 | 2 |
| C3×#63431 | 2 |
| #11720516 | 2 |
| #11720297 | 2 |
| #11720294 | 2 |
| #10590280 | 3 |
| #10588734 | 3 |