Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
236 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 81 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×#817 | C2 | semidirect |
| 3. C9×#812 | C2 | semidirect |
| 7. C3×C9×Q16 | C4 | semidirect |
| 9. C3×C9×D8 | C4 | semidirect |
| 29. #4566 | C9 | direct (N × H) |
| 40. C9×Q16 | Dic3 | semidirect |
| 44. C9×D8 | Dic3 | semidirect |
| 60. #817 | C2×C9 | semidirect |
| 61. #812 | C2×C9 | semidirect |
| 93. C3×Q16 | C4×C9 | semidirect |
| 99. C3×D8 | C4×C9 | semidirect |
| 128. C3×C9 | #360 | semidirect |
| 162. Q16 | C9×Dic3 | semidirect |
| 164. D8 | C9×Dic3 | semidirect |
| 187. C9 | #4566 | direct (N × H) |
| 212. C3 | C9×#360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#135 | 2 |
| C9×#817 | 2 |
| C9×#812 | 2 |
| C3×#4566 | 3 |
| C9×#360 | 3 |