Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×C3×Dic9 | C2 | semidirect |
| 3. C2×D3×Dic9 | C2 | semidirect |
| 4. #88551 | C2 | semidirect |
| 5. (C2×D3)⋊Dic9 | C2 | semidirect |
| 6. Dic3⋊Dic9 | C2 | semidirect |
| 7. Dic3×Dic9 | C2 | semidirect |
| 14. C9×#67 | C4 | semidirect |
| 29. C22×Dic9 | D3 | semidirect |
| 37. C22×C3×C9 | C2×C4 | semidirect |
| 41. C2×D3×C9 | C2×C4 | semidirect |
| 44. C9×Dic3 | C2×C4 | semidirect |
| 46. C3×Dic9 | D4 | semidirect |
| 113. C22×C9 | C4×D3 | semidirect |
| 121. Dic9 | #67 | direct (N × H) |
| 123. C3×C9 | C4×D4 | semidirect |
| 134. #67 | Dic9 | direct (N × H) |
| 179. C22×C3 | C2×Dic9 | semidirect |
| 185. C2×D3 | C2×Dic9 | semidirect |
| 197. Dic3 | C2×Dic9 | semidirect |
| 200. C9 | C4×#67 | semidirect |
| 230. C22 | D3×Dic9 | semidirect |
| 238. 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×#67 | 2 |
| C22×C3×Dic9 | 2 |
| C2×D3×Dic9 | 2 |
| #88551 | 2 |
| (C2×D3)⋊Dic9 | 2 |
| Dic3⋊Dic9 | 2 |
| Dic3×Dic9 | 2 |
| Dic3×#67 | 3 |
| D4×Dic9 | 3 |