Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
470 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×C9×#204 | C2 | semidirect |
| 3. C9×#869 | C2 | semidirect |
| 4. C3×C4×C8×C9 | C2 | semidirect |
| 22. C4×C8×C9 | D3 | semidirect |
| 30. C3×C8×C9 | D4 | semidirect |
| 32. #4693 | C9 | direct (N × H) |
| 52. C3×C4×C9 | SD16 | semidirect |
| 58. C2×#204 | C2×C9 | semidirect |
| 60. #869 | C2×C9 | semidirect |
| 62. C3×C4×C8 | C2×C9 | semidirect |
| 82. C8×C9 | D12 | semidirect |
| 116. C4×C9 | #204 | semidirect |
| 121. C4×C8 | D3×C9 | semidirect |
| 122. C3×C9 | #492 | semidirect |
| 140. C3×C8 | D4×C9 | semidirect |
| 167. C3×C4 | C9×SD16 | semidirect |
| 174. C9 | #4693 | direct (N × H) |
| 182. C8 | C9×D12 | semidirect |
| 195. C4 | C9×#204 | semidirect |
| 198. C3 | C9×#492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#204 | 2 |
| C9×#874 | 2 |
| C9×#869 | 2 |
| C3×C4×C8×C9 | 2 |
| C3×#4693 | 3 |
| C9×#492 | 3 |