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. #10624194 | C2 | semidirect |
| 2. C8×C3⋊D15 | C2 | semidirect |
| 3. C3×D120 | C2 | semidirect |
| 4. C3×C5×Dic12 | C2 | semidirect |
| 5. #10623801 | C2 | semidirect |
| 20. D120 | D3 | semidirect |
| 24. C5×Dic12 | D3 | semidirect |
| 35. C3×Dic12 | D5 | semidirect |
| 91. Dic12 | D15 | semidirect |
| 96. C32×C5 | #135 | semidirect |
| 149. C3×C5 | #912 | semidirect |
| 150. C3×C5 | #919 | semidirect |
| 167. C32 | #4065 | semidirect |
| 183. C5 | #63810 | semidirect |
| 190. C3 | #91277 | semidirect |
| 191. C3 | #91808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624194 | 2 |
| C8×C3⋊D15 | 2 |
| C3×D120 | 2 |
| C3×C5×Dic12 | 2 |
| #10623801 | 2 |
| #91808 | 3 |
| #91277 | 3 |
| #63810 | 5 |