Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
336 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 336 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. C22×C3×C4×C9 | C2 | semidirect |
| 2. C2×C9×#67 | C2 | semidirect |
| 3. C2×C9×D12 | C2 | semidirect |
| 4. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C9×C4⋊Dic3 | C2 | semidirect |
| 24. C22×C4×C9 | D3 | semidirect |
| 29. C22×C3×C9 | D4 | semidirect |
| 35. C3×C4×C9 | D4 | semidirect |
| 38. #930 | C9 | direct (N × H) |
| 67. C22×C3×C4 | C2×C9 | semidirect |
| 69. C2×#67 | C2×C9 | semidirect |
| 70. C2×D12 | C2×C9 | semidirect |
| 73. (C2×D3)⋊C4 | C2×C9 | semidirect |
| 74. C4⋊Dic3 | C2×C9 | semidirect |
| 94. C22×C9 | D12 | semidirect |
| 100. C4×C9 | #67 | semidirect |
| 102. C3×C9 | #121 | semidirect |
| 139. C22×C4 | D3×C9 | semidirect |
| 153. C22×C3 | D4×C9 | semidirect |
| 165. C3×C4 | D4×C9 | semidirect |
| 170. C9 | #930 | direct (N × H) |
| 198. C22 | C9×D12 | semidirect |
| 202. C4 | C9×#67 | semidirect |
| 204. C3 | C9×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C9 | 2 |
| C2×C9×#67 | 2 |
| C2×C9×D12 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C9×C4⋊Dic3 | 2 |
| C3×#930 | 3 |
| C9×#121 | 3 |