Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
250 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×C9×D12 | C2 | semidirect |
| 2. C2×C3×C8×C9 | C2 | semidirect |
| 3. C9×D24 | C2 | direct (N × H) |
| 9. C9×D12 | C22 | semidirect |
| 10. C3×C8×C9 | C22 | semidirect |
| 17. C2×C8×C9 | D3 | semidirect |
| 24. C2×D24 | C9 | direct (N × H) |
| 36. C8×C9 | C2×D3 | semidirect |
| 37. C2×C3×C9 | D8 | semidirect |
| 41. C2×D12 | C2×C9 | semidirect |
| 44. C2×C3×C8 | C2×C9 | semidirect |
| 46. D24 | C2×C9 | direct (N × H) |
| 61. C3×C9 | C2×D8 | semidirect |
| 70. D12 | C22×C9 | semidirect |
| 72. C3×C8 | C22×C9 | semidirect |
| 80. C2×C9 | D24 | direct (N × H) |
| 84. C2×C8 | D3×C9 | semidirect |
| 100. C9 | C2×D24 | direct (N × H) |
| 105. C8 | C2×D3×C9 | semidirect |
| 109. C2×C3 | C9×D8 | semidirect |
| 120. C3 | C2×C9×D8 | semidirect |
| 123. C2 | C9×D24 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D12 | 2 |
| C2×C3×C8×C9 | 2 |
| C9×D24 | 2 |
| C2×C3×D24 | 3 |
| C2×C9×D8 | 3 |