Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
550 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. C9×#1004 | C2 | semidirect |
| 2. C9×#940 | C2 | semidirect |
| 3. C9×#908 | C2 | semidirect |
| 4. C3×C9×#100 | C2 | semidirect |
| 5. C9×#825 | C2 | semidirect |
| 14. C2×C9×D12 | C22 | semidirect |
| 15. C3×C9×M16 | C22 | semidirect |
| 16. C4×C9×Dic3 | C22 | semidirect |
| 29. C9×#100 | D3 | semidirect |
| 41. C9×D12 | D4 | semidirect |
| 43. C9×Dic6 | D4 | semidirect |
| 46. #4747 | C9 | direct (N × H) |
| 69. C9×M16 | C2×D3 | semidirect |
| 82. #1004 | C2×C9 | semidirect |
| 85. #940 | C2×C9 | semidirect |
| 86. #908 | C2×C9 | semidirect |
| 89. C3×#100 | C2×C9 | semidirect |
| 91. #825 | C2×C9 | semidirect |
| 146. C2×D12 | C22×C9 | semidirect |
| 150. C3×M16 | C22×C9 | semidirect |
| 153. C4×Dic3 | C22×C9 | semidirect |
| 184. #100 | D3×C9 | semidirect |
| 185. C3×C9 | #453 | semidirect |
| 214. D12 | D4×C9 | semidirect |
| 216. Dic6 | D4×C9 | semidirect |
| 242. M16 | C2×D3×C9 | semidirect |
| 270. C9 | #4747 | direct (N × H) |
| 310. C3 | C9×#453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1004 | 2 |
| C9×#940 | 2 |
| C9×#908 | 2 |
| C3×C9×#100 | 2 |
| C9×#825 | 2 |
| C3×#4747 | 3 |
| C9×#453 | 3 |