Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 122 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. C4×C3⋊Dic15 | C2 | semidirect |
| 3. C3×C4×Dic15 | C2 | semidirect |
| 4. Dic3⋊Dic15 | C2 | semidirect |
| 13. C3×C4×C5×D3 | C4 | semidirect |
| 22. C4×Dic15 | D3 | semidirect |
| 51. C4×C5×D3 | Dic3 | semidirect |
| 68. C3×C4×D3 | Dic5 | semidirect |
| 97. C32×C5 | #117 | semidirect |
| 133. C4×D3 | Dic15 | semidirect |
| 150. C3×C5 | #872 | semidirect |
| 151. C3×C5 | #926 | semidirect |
| 172. C32 | #4072 | semidirect |
| 187. C5 | #63855 | semidirect |
| 196. C3 | #91371 | semidirect |
| 197. C3 | #91815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C5×D3 | 2 |
| C4×C3⋊Dic15 | 2 |
| C3×C4×Dic15 | 2 |
| Dic3⋊Dic15 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| #91815 | 3 |
| #91371 | 3 |
| #63855 | 5 |