Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
196 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 60 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. #10623904 | C2 | semidirect |
| 3. C3×C4×C5×Dic3 | C2 | semidirect |
| 8. C3×D60 | C4 | semidirect |
| 10. C3×Dic30 | C4 | semidirect |
| 20. C4×C5×Dic3 | D3 | semidirect |
| 30. C3×C4×Dic3 | D5 | semidirect |
| 36. D60 | Dic3 | semidirect |
| 38. Dic30 | Dic3 | semidirect |
| 80. C4×Dic3 | D15 | semidirect |
| 84. C32×C5 | #104 | semidirect |
| 136. C3×C5 | #805 | semidirect |
| 137. C3×C5 | #837 | semidirect |
| 156. C32 | #3937 | semidirect |
| 172. C5 | #63569 | semidirect |
| 180. C3 | #90977 | semidirect |
| 181. C3 | #91089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6817 | 2 |
| #10623904 | 2 |
| C3×C4×C5×Dic3 | 2 |
| #91089 | 3 |
| #90977 | 3 |
| #63569 | 5 |