Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
208 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 208 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×#237 | C2 | semidirect |
| 2. C3×C9×D8 | C2 | semidirect |
| 3. C9×#214 | C2 | semidirect |
| 4. C9×Dic12 | C2 | semidirect |
| 5. D3×C8×C9 | C2 | semidirect |
| 24. C9×D8 | D3 | semidirect |
| 32. #912 | C9 | direct (N × H) |
| 53. #237 | C2×C9 | semidirect |
| 57. C3×D8 | C2×C9 | semidirect |
| 60. #214 | C2×C9 | semidirect |
| 61. Dic12 | C2×C9 | semidirect |
| 62. D3×C8 | C2×C9 | semidirect |
| 76. C3×C9 | #135 | semidirect |
| 104. D8 | D3×C9 | semidirect |
| 120. C9 | #912 | direct (N × H) |
| 142. C3 | C9×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#237 | 2 |
| C3×C9×D8 | 2 |
| C9×#214 | 2 |
| C9×Dic12 | 2 |
| D3×C8×C9 | 2 |
| C3×#912 | 3 |
| C9×#135 | 3 |