Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
438 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 438 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. C9×#870 | C2 | semidirect |
| 3. C3×#63362 | C2 | semidirect |
| 4. #11720267 | C2 | semidirect |
| 21. #63362 | D3 | semidirect |
| 56. #870 | D9 | semidirect |
| 120. C3×C9 | #490 | semidirect |
| 174. C9 | #4713 | semidirect |
| 198. C3 | #10588748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721711 | 2 |
| C9×#870 | 2 |
| C3×#63362 | 2 |
| #11720267 | 2 |
| #10590282 | 3 |
| #10588748 | 3 |