Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
506 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 167 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×#6226 | C2 | semidirect |
| 3. C2×C3×Dic18 | C2 | semidirect |
| 5. C2×#6189 | C2 | semidirect |
| 6. D3×Dic18 | C2 | direct (N × H) |
| 12. #6226 | C22 | semidirect |
| 16. C3×Dic18 | C22 | semidirect |
| 18. #6189 | C22 | semidirect |
| 31. C2×Dic18 | D3 | direct (N × H) |
| 33. C2×D3×C9 | Q8 | semidirect |
| 63. Dic18 | C2×D3 | direct (N × H) |
| 64. C2×C3×C9 | C2×Q8 | semidirect |
| 66. D3×C9 | C2×Q8 | semidirect |
| 98. C3×C9 | C22×Q8 | semidirect |
| 128. C2×C9 | D3×Q8 | semidirect |
| 141. C2×D3 | Dic18 | direct (N × H) |
| 155. C9 | C2×D3×Q8 | semidirect |
| 169. C2×C3 | C2×Dic18 | semidirect |
| 173. D3 | C2×Dic18 | direct (N × H) |
| 182. C3 | C22×Dic18 | semidirect |
| 185. C2 | D3×Dic18 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6226 | 2 |
| C2×C4×D3×C9 | 2 |
| C2×C3×Dic18 | 2 |
| C2×D3×Dic9 | 2 |
| C2×#6189 | 2 |
| D3×Dic18 | 2 |
| C2×D3×Dic6 | 3 |
| C22×Dic18 | 3 |