Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
424 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 424 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. C23×D3×C9 | C2 | semidirect |
| 2. C2×C9×#67 | C2 | semidirect |
| 3. C2×C9×D12 | C2 | semidirect |
| 4. C3×C9×C22⋊C4 | C2 | semidirect |
| 5. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 12. C22×D3×C9 | C22 | semidirect |
| 13. C2×C3×C4×C9 | C22 | semidirect |
| 15. C2×C9×Dic3 | C22 | semidirect |
| 27. C9×C22⋊C4 | D3 | semidirect |
| 29. C22×C3×C9 | D4 | semidirect |
| 36. C2×D3×C9 | D4 | semidirect |
| 40. #882 | C9 | direct (N × H) |
| 60. C2×C4×C9 | C2×D3 | semidirect |
| 67. C23×D3 | C2×C9 | semidirect |
| 70. C2×#67 | C2×C9 | semidirect |
| 71. C2×D12 | C2×C9 | semidirect |
| 74. C3×C22⋊C4 | C2×C9 | semidirect |
| 76. (C2×D3)⋊C4 | C2×C9 | semidirect |
| 98. C22×C9 | D12 | semidirect |
| 104. C3×C9 | #120 | semidirect |
| 115. C22×D3 | C22×C9 | semidirect |
| 120. C2×C3×C4 | C22×C9 | semidirect |
| 123. C2×Dic3 | C22×C9 | semidirect |
| 142. C22⋊C4 | D3×C9 | semidirect |
| 154. C22×C3 | D4×C9 | semidirect |
| 163. C2×D3 | D4×C9 | semidirect |
| 171. C9 | #882 | direct (N × H) |
| 180. C2×C4 | C2×D3×C9 | semidirect |
| 201. C22 | C9×D12 | semidirect |
| 206. C3 | C9×#120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D3×C9 | 2 |
| C2×C9×#67 | 2 |
| C2×C9×D12 | 2 |
| C3×C9×C22⋊C4 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C3×#882 | 3 |
| C9×#120 | 3 |