Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
210 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 45 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. C9×#217 | C2 | semidirect |
| 3. C3×#3676 | C2 | semidirect |
| 7. C22×C3⋊D9 | C4 | semidirect |
| 10. C2×C3⋊Dic9 | C4 | semidirect |
| 19. #3676 | D3 | semidirect |
| 61. #217 | D9 | semidirect |
| 88. C3×C9 | #99 | semidirect |
| 153. C9 | #806 | semidirect |
| 186. C3 | #63365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6233 | 2 |
| C9×#217 | 2 |
| C3×#3676 | 2 |
| #63581 | 3 |
| #63365 | 3 |