Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11720572 | C2 | semidirect |
| 3. C3×#63389 | C2 | semidirect |
| 9. C2×C9×D12 | C4 | semidirect |
| 11. C9×C4⋊Dic3 | C4 | semidirect |
| 19. #63389 | D3 | semidirect |
| 119. C2×D12 | Dic9 | semidirect |
| 124. C4⋊Dic3 | Dic9 | semidirect |
| 161. C3×C9 | #327 | semidirect |
| 253. C9 | #4470 | semidirect |
| 297. C3 | #10588214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#930 | 2 |
| #11720572 | 2 |
| C3×#63389 | 2 |
| #10589150 | 3 |
| #10588214 | 3 |