Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
156 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 156 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. #10623611 | C2 | semidirect |
| 3. C9×C22⋊Dic5 | C2 | semidirect |
| 6. C22×C5×D9 | C4 | semidirect |
| 10. C2×C5×Dic9 | C4 | semidirect |
| 44. C22⋊Dic5 | D9 | semidirect |
| 46. C22×D9 | Dic5 | semidirect |
| 51. C2×Dic9 | Dic5 | semidirect |
| 64. C5×C9 | #99 | semidirect |
| 126. C9 | #3966 | semidirect |
| 139. C5 | #63365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#611 | 2 |
| #10623611 | 2 |
| C9×C22⋊Dic5 | 2 |
| #90996 | 3 |
| #63365 | 5 |