Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
136 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 69 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×C4×C9 | C2 | semidirect |
| 2. C9×#67 | C2 | semidirect |
| 3. C9×D12 | C2 | semidirect |
| 4. C4×D3×C9 | C2 | semidirect |
| 5. C9×Dic6 | C2 | semidirect |
| 23. C2×C4×C9 | D3 | semidirect |
| 28. #235 | C9 | direct (N × H) |
| 42. C3×C9 | #41 | semidirect |
| 48. C2×C3×C4 | C2×C9 | semidirect |
| 50. #67 | C2×C9 | semidirect |
| 51. D12 | C2×C9 | semidirect |
| 52. C4×D3 | C2×C9 | semidirect |
| 53. Dic6 | C2×C9 | semidirect |
| 78. C9 | #235 | direct (N × H) |
| 83. C2×C4 | D3×C9 | semidirect |
| 98. C3 | C9×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C9 | 2 |
| C9×#67 | 2 |
| C9×D12 | 2 |
| C4×D3×C9 | 2 |
| C9×Dic6 | 2 |
| C3×#235 | 3 |
| C9×#41 | 3 |