Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 1. #10624196 | C2 | semidirect |
| 2. C8×C3⋊D15 | C2 | semidirect |
| 3. C3×Dic60 | C2 | semidirect |
| 4. C3×C5×D24 | C2 | semidirect |
| 5. #10623802 | C2 | semidirect |
| 20. Dic60 | D3 | semidirect |
| 24. C5×D24 | D3 | semidirect |
| 36. C3×D24 | D5 | semidirect |
| 92. D24 | D15 | semidirect |
| 96. C32×C5 | #135 | semidirect |
| 149. C3×C5 | #912 | semidirect |
| 150. C3×C5 | #919 | semidirect |
| 167. C32 | #4058 | semidirect |
| 183. C5 | #63810 | semidirect |
| 190. C3 | #91279 | semidirect |
| 191. C3 | #91801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624196 | 2 |
| C8×C3⋊D15 | 2 |
| C3×Dic60 | 2 |
| C3×C5×D24 | 2 |
| #10623802 | 2 |
| #91801 | 3 |
| #91279 | 3 |
| #63810 | 5 |