Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
244 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 244 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. C3×C9×#41 | C2 | semidirect |
| 2. C2×C9×D12 | C2 | semidirect |
| 3. C9×#215 | C2 | semidirect |
| 4. C9×#213 | C2 | semidirect |
| 5. C9×#208 | C2 | semidirect |
| 9. C3×Q8×C9 | C22 | semidirect |
| 11. C3×D4×C9 | C22 | semidirect |
| 16. C9×C3⋊C8 | C22 | semidirect |
| 23. C9×#41 | D3 | semidirect |
| 36. #949 | C9 | direct (N × H) |
| 48. Q8×C9 | C2×D3 | semidirect |
| 54. D4×C9 | C2×D3 | semidirect |
| 65. C3×#41 | C2×C9 | semidirect |
| 68. C2×D12 | C2×C9 | semidirect |
| 72. #215 | C2×C9 | semidirect |
| 73. #213 | C2×C9 | semidirect |
| 74. #208 | C2×C9 | semidirect |
| 95. C3×C9 | AGL(1,ℤ/8) | semidirect |
| 99. C3×Q8 | C22×C9 | semidirect |
| 107. C3×D4 | C22×C9 | semidirect |
| 118. C3⋊C8 | C22×C9 | semidirect |
| 130. #41 | D3×C9 | semidirect |
| 156. C9 | #949 | direct (N × H) |
| 158. Q8 | C2×D3×C9 | semidirect |
| 162. D4 | C2×D3×C9 | semidirect |
| 185. 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 |
|---|---|
| C3×C9×#41 | 2 |
| C2×C9×D12 | 2 |
| C9×#215 | 2 |
| C9×#213 | 2 |
| C9×#208 | 2 |
| C3×#949 | 3 |
| C9×AGL(1,ℤ/8) | 3 |