Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
296 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 65 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. D9×Dic12 | C2 | semidirect |
| 3. #11720564 | C2 | semidirect |
| 4. C9×#827 | C2 | semidirect |
| 5. #11720242 | C2 | semidirect |
| 6. #11720233 | C2 | semidirect |
| 7. D9×C3⋊C16 | C2 | semidirect |
| 13. #88521 | C22 | semidirect |
| 15. C9×Dic12 | C22 | semidirect |
| 19. C3⋊(C9⋊C16) | C22 | semidirect |
| 20. C9×C3⋊C16 | C22 | semidirect |
| 93. #827 | D9 | direct (N × H) |
| 126. C3×D9 | SD32 | semidirect |
| 144. Dic12 | C2×D9 | semidirect |
| 151. C3⋊C16 | C2×D9 | semidirect |
| 178. C3×C9 | C2×SD32 | semidirect |
| 213. D9 | #827 | direct (N × H) |
| 246. C9 | C2×#827 | semidirect |
| 277. C3 | D9×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D8×D9 | 2 |
| D9×Dic12 | 2 |
| #11720564 | 2 |
| C9×#827 | 2 |
| #11720242 | 2 |
| #11720233 | 2 |
| D9×C3⋊C16 | 2 |
| D3×#827 | 3 |
| D9×SD32 | 3 |