Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
310 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 63 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×C9×#99 | C2 | semidirect |
| 3. C9×#834 | C2 | semidirect |
| 9. C2×C9×D12 | C4 | semidirect |
| 12. C4×C9×Dic3 | C4 | semidirect |
| 19. C9×#99 | D3 | semidirect |
| 32. #4474 | C9 | direct (N × H) |
| 65. C3×#99 | C2×C9 | semidirect |
| 67. #834 | C2×C9 | semidirect |
| 109. C2×D12 | C4×C9 | semidirect |
| 116. C4×Dic3 | C4×C9 | semidirect |
| 150. #99 | D3×C9 | semidirect |
| 151. C3×C9 | #353 | semidirect |
| 233. C9 | #4474 | direct (N × H) |
| 272. C3 | C9×#353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#940 | 2 |
| C3×C9×#99 | 2 |
| C9×#834 | 2 |
| C3×#4474 | 3 |
| C9×#353 | 3 |