Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 136 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. C3×C4×Dic15 | C2 | semidirect |
| 3. C32×C4×Dic5 | C2 | semidirect |
| 4. C3×Dic3⋊Dic5 | C2 | semidirect |
| 7. #91371 | C3 | direct (N × H) |
| 12. C3×C4×C5×D3 | C4 | semidirect |
| 17. C4×Dic15 | C2×C3 | semidirect |
| 22. C3×C4×Dic5 | D3 | semidirect |
| 23. C3×C4×Dic5 | C2×C3 | semidirect |
| 24. Dic3⋊Dic5 | C2×C3 | semidirect |
| 48. C4×C5×D3 | C3×C4 | semidirect |
| 62. C4×Dic5 | C3×D3 | semidirect |
| 68. C3×C4×D3 | Dic5 | semidirect |
| 97. C32×C5 | #117 | semidirect |
| 133. C4×D3 | C3×Dic5 | semidirect |
| 150. C3×C5 | #872 | semidirect |
| 151. C3×C5 | C3×#117 | semidirect |
| 172. C32 | #4072 | semidirect |
| 187. C5 | C3×#872 | semidirect |
| 196. C3 | #91371 | direct (N × H) |
| 197. C3 | C3×#4072 | 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 |
| C3×C4×Dic15 | 2 |
| C32×C4×Dic5 | 2 |
| C3×Dic3⋊Dic5 | 2 |
| C3×(C2×D3)⋊Dic5 | 2 |
| C3×#4072 | 3 |
| #91371 | 3 |
| C3×#872 | 5 |