Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
156 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 49 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. C5×#3676 | C2 | semidirect |
| 6. C22×C9×D5 | C4 | semidirect |
| 11. C2×C9×Dic5 | C4 | semidirect |
| 28. #3676 | D5 | semidirect |
| 64. C5×C9 | #99 | semidirect |
| 66. C22×D5 | Dic9 | semidirect |
| 71. C2×Dic5 | Dic9 | semidirect |
| 126. C9 | #3938 | semidirect |
| 139. C5 | #63393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×C22⋊D5 | 2 |
| #10623611 | 2 |
| C5×#3676 | 2 |
| #90995 | 3 |
| #63393 | 5 |