Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. C2×D3×Dic9 | C2 | semidirect |
| 3. C4×C3⋊Dic9 | C2 | semidirect |
| 4. C3×C4⋊Dic9 | C2 | semidirect |
| 5. (C2×D3)⋊Dic9 | C2 | semidirect |
| 13. C9×D12 | C4 | semidirect |
| 23. C4⋊Dic9 | D3 | semidirect |
| 29. C2×D3×C9 | C2×C4 | semidirect |
| 30. C3×C4×C9 | C2×C4 | semidirect |
| 32. C3⋊Dic9 | D4 | semidirect |
| 82. C4×C9 | C4×D3 | semidirect |
| 89. C3×C9 | C4×D4 | semidirect |
| 105. D12 | Dic9 | semidirect |
| 131. C2×D3 | C2×Dic9 | semidirect |
| 134. C3×C4 | C2×Dic9 | semidirect |
| 145. C9 | #893 | semidirect |
| 171. C4 | D3×Dic9 | semidirect |
| 173. C3 | D4×Dic9 | 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×D3×Dic9 | 2 |
| C4×C3⋊Dic9 | 2 |
| C3×C4⋊Dic9 | 2 |
| (C2×D3)⋊Dic9 | 2 |
| #63898 | 3 |
| D4×Dic9 | 3 |