Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
530 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 267 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×C3×Q8×C9 | C2 | semidirect |
| 2. C9×#239 | C2 | direct (N × H) |
| 3. C2×C9×D12 | C2 | semidirect |
| 4. C2×C4×D3×C9 | C2 | semidirect |
| 8. C3×Q8×C9 | C22 | semidirect |
| 11. C9×D12 | C22 | semidirect |
| 12. C4×D3×C9 | C22 | semidirect |
| 19. C2×Q8×C9 | D3 | semidirect |
| 28. C2×#239 | C9 | direct (N × H) |
| 37. Q8×C9 | C2×D3 | semidirect |
| 43. C2×C3×C9 | #41 | semidirect |
| 48. C2×C3×Q8 | C2×C9 | semidirect |
| 52. #239 | C2×C9 | direct (N × H) |
| 53. C2×D12 | C2×C9 | semidirect |
| 54. C2×C4×D3 | C2×C9 | semidirect |
| 68. C3×C9 | C2×#41 | semidirect |
| 72. C3×Q8 | C22×C9 | semidirect |
| 81. D12 | C22×C9 | semidirect |
| 82. C4×D3 | C22×C9 | semidirect |
| 89. C2×C9 | #239 | direct (N × H) |
| 92. C2×Q8 | D3×C9 | semidirect |
| 109. C9 | C2×#239 | direct (N × H) |
| 111. Q8 | C2×D3×C9 | semidirect |
| 119. C2×C3 | C9×#41 | semidirect |
| 130. C3 | C2×C9×#41 | semidirect |
| 133. C2 | C9×#239 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C9 | 2 |
| C9×#239 | 2 |
| C2×C9×D12 | 2 |
| C2×C4×D3×C9 | 2 |
| C2×C3×#239 | 3 |
| C2×C9×#41 | 3 |