Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
204 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 204 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 |
|---|---|---|
| 1. C9×#239 | C2 | semidirect |
| 2. C3×C9×Q16 | C2 | semidirect |
| 3. C9×#215 | C2 | semidirect |
| 4. C9×D24 | C2 | semidirect |
| 5. D3×C8×C9 | C2 | semidirect |
| 22. C9×Q16 | D3 | semidirect |
| 32. #919 | C9 | direct (N × H) |
| 53. #239 | C2×C9 | semidirect |
| 55. C3×Q16 | C2×C9 | semidirect |
| 60. #215 | C2×C9 | semidirect |
| 61. D24 | C2×C9 | semidirect |
| 62. D3×C8 | C2×C9 | semidirect |
| 76. C3×C9 | #135 | semidirect |
| 101. Q16 | D3×C9 | semidirect |
| 119. C9 | #919 | direct (N × H) |
| 140. C3 | C9×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#239 | 2 |
| C3×C9×Q16 | 2 |
| C9×#215 | 2 |
| C9×D24 | 2 |
| D3×C8×C9 | 2 |
| C3×#919 | 3 |
| C9×#135 | 3 |