Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
502 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 502 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 |
|---|---|---|
| 2. C9×#936 | C2 | semidirect |
| 3. C9×#909 | C2 | semidirect |
| 4. C3×C9×#100 | C2 | semidirect |
| 5. C9×#825 | C2 | semidirect |
| 13. C2×C9×Dic6 | C22 | semidirect |
| 14. C3×C9×M16 | C22 | semidirect |
| 16. C4×C9×Dic3 | C22 | semidirect |
| 29. C9×#100 | D3 | semidirect |
| 45. #4746 | C9 | direct (N × H) |
| 67. C9×M16 | C2×D3 | semidirect |
| 83. #936 | C2×C9 | semidirect |
| 84. #909 | C2×C9 | semidirect |
| 87. C3×#100 | C2×C9 | semidirect |
| 89. #825 | C2×C9 | semidirect |
| 139. C2×Dic6 | C22×C9 | semidirect |
| 143. C3×M16 | C22×C9 | semidirect |
| 148. C4×Dic3 | C22×C9 | semidirect |
| 177. #100 | D3×C9 | semidirect |
| 178. C3×C9 | #455 | semidirect |
| 230. M16 | C2×D3×C9 | semidirect |
| 257. C9 | #4746 | direct (N × H) |
| 293. C3 | C9×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1004 | 2 |
| C9×#936 | 2 |
| C9×#909 | 2 |
| C3×C9×#100 | 2 |
| C9×#825 | 2 |
| C3×#4746 | 3 |
| C9×#455 | 3 |