Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
208 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 87 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×#235 | C2 | semidirect |
| 2. C2×C3×C8×C9 | C2 | semidirect |
| 3. C9×Dic12 | C2 | semidirect |
| 4. C9×D24 | C2 | semidirect |
| 5. C9×#204 | C2 | semidirect |
| 25. C2×C8×C9 | D3 | semidirect |
| 32. #904 | C9 | direct (N × H) |
| 54. #235 | C2×C9 | semidirect |
| 59. C2×C3×C8 | C2×C9 | semidirect |
| 61. Dic12 | C2×C9 | semidirect |
| 62. D24 | C2×C9 | semidirect |
| 63. #204 | C2×C9 | semidirect |
| 78. C3×C9 | #135 | semidirect |
| 108. C2×C8 | D3×C9 | semidirect |
| 124. C9 | #904 | direct (N × H) |
| 146. C3 | C9×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#235 | 2 |
| C2×C3×C8×C9 | 2 |
| C9×Dic12 | 2 |
| C9×D24 | 2 |
| C9×#204 | 2 |
| C3×#904 | 3 |
| C9×#135 | 3 |