Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 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×D4×C9 | C2 | semidirect |
| 2. C2×C9×#67 | C2 | semidirect |
| 3. C2×C9×D12 | C2 | semidirect |
| 4. C4×C9×Dic3 | C2 | semidirect |
| 21. C2×D4×C9 | D3 | semidirect |
| 28. C3×C4×C9 | D4 | semidirect |
| 29. C9×Dic3 | D4 | semidirect |
| 31. #940 | C9 | direct (N × H) |
| 56. C2×C3×D4 | C2×C9 | semidirect |
| 58. C2×#67 | C2×C9 | semidirect |
| 59. C2×D12 | C2×C9 | semidirect |
| 61. C4×Dic3 | C2×C9 | semidirect |
| 79. C4×C9 | #67 | semidirect |
| 81. C3×C9 | #127 | semidirect |
| 112. C2×D4 | D3×C9 | semidirect |
| 129. C3×C4 | D4×C9 | semidirect |
| 131. Dic3 | D4×C9 | semidirect |
| 134. C9 | #940 | direct (N × H) |
| 159. C4 | C9×#67 | semidirect |
| 161. C3 | C9×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C9 | 2 |
| C2×C9×#67 | 2 |
| C2×C9×D12 | 2 |
| C4×C9×Dic3 | 2 |
| C3×#940 | 3 |
| C9×#127 | 3 |