Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
342 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 1. C2×#67180 | C2 | semidirect |
| 3. C3×C4×Dic15 | C2 | semidirect |
| 4. (C2×D3)⋊Dic15 | C2 | semidirect |
| 20. C4×Dic15 | D3 | semidirect |
| 88. C32×C5 | #124 | semidirect |
| 139. C3×C5 | #875 | semidirect |
| 140. C3×C5 | #936 | semidirect |
| 159. C32 | #4082 | semidirect |
| 174. C5 | #63860 | semidirect |
| 182. C3 | #91373 | semidirect |
| 183. C3 | #91825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67180 | 2 |
| C2×C3×C5×D12 | 2 |
| C3×C4×Dic15 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| #91825 | 3 |
| #91373 | 3 |
| #63860 | 5 |