Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
190 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 47 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. #88551 | C2 | semidirect |
| 3. C9×#217 | C2 | semidirect |
| 7. C22×C3×D9 | C4 | semidirect |
| 12. C2×C3×Dic9 | C4 | semidirect |
| 40. C22×D9 | Dic3 | semidirect |
| 46. C2×Dic9 | Dic3 | semidirect |
| 58. #217 | D9 | semidirect |
| 83. C3×C9 | #99 | semidirect |
| 142. C9 | #834 | semidirect |
| 174. C3 | #63365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#611 | 2 |
| #88551 | 2 |
| C9×#217 | 2 |
| #63580 | 3 |
| #63365 | 3 |