Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
308 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 105 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×C9×D12 | C2 | semidirect |
| 3. C2×C4×D3×C9 | C2 | semidirect |
| 4. C3×C9×C4⋊C4 | C2 | semidirect |
| 5. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 25. C9×C4⋊C4 | D3 | semidirect |
| 33. C2×D3×C9 | D4 | semidirect |
| 35. C3×C4×C9 | D4 | semidirect |
| 38. #895 | C9 | direct (N × H) |
| 65. C2×D12 | C2×C9 | semidirect |
| 66. C2×D12 | C2×C9 | semidirect |
| 67. C2×C4×D3 | C2×C9 | semidirect |
| 69. C3×C4⋊C4 | C2×C9 | semidirect |
| 72. (C2×D3)⋊C4 | C2×C9 | semidirect |
| 95. C4×C9 | D12 | semidirect |
| 97. C3×C9 | #121 | semidirect |
| 132. C4⋊C4 | D3×C9 | semidirect |
| 148. C2×D3 | D4×C9 | semidirect |
| 154. C3×C4 | D4×C9 | semidirect |
| 159. C9 | #895 | direct (N × H) |
| 190. C4 | C9×D12 | semidirect |
| 192. C3 | C9×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D12 | 2 |
| C2×C4×D3×C9 | 2 |
| C3×C9×C4⋊C4 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C3×#895 | 3 |
| C9×#121 | 3 |