Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
224 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 224 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×C9×D12 | C2 | semidirect |
| 3. C3×C9×M16 | C2 | semidirect |
| 4. C9×D24 | C2 | semidirect |
| 5. C9×#204 | C2 | semidirect |
| 13. C9×D12 | C22 | semidirect |
| 15. C9×Dic6 | C22 | semidirect |
| 16. C3×C8×C9 | C22 | semidirect |
| 27. C9×M16 | D3 | semidirect |
| 36. #908 | C9 | direct (N × H) |
| 56. C8×C9 | C2×D3 | semidirect |
| 63. #235 | C2×C9 | semidirect |
| 64. C2×D12 | C2×C9 | semidirect |
| 68. C3×M16 | C2×C9 | semidirect |
| 70. D24 | C2×C9 | semidirect |
| 71. #204 | C2×C9 | semidirect |
| 90. C3×C9 | AGL(1,ℤ/8) | semidirect |
| 105. D12 | C22×C9 | semidirect |
| 107. Dic6 | C22×C9 | semidirect |
| 109. C3×C8 | C22×C9 | semidirect |
| 125. M16 | D3×C9 | semidirect |
| 145. C9 | #908 | direct (N × H) |
| 154. C8 | C2×D3×C9 | semidirect |
| 173. C3 | C9×AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#235 | 2 |
| C2×C9×D12 | 2 |
| C3×C9×M16 | 2 |
| C9×D24 | 2 |
| C9×#204 | 2 |
| C3×#908 | 3 |
| C9×AGL(1,ℤ/8) | 3 |