Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
258 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 63 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. C5×#3746 | C2 | semidirect |
| 3. C3×Dic60 | C2 | semidirect |
| 5. #10623826 | C2 | semidirect |
| 18. Dic60 | D3 | semidirect |
| 34. #3746 | D5 | semidirect |
| 57. C3×D15 | Q16 | semidirect |
| 93. C32×C5 | C2×Q16 | semidirect |
| 110. D15 | Dic12 | semidirect |
| 141. C3×C5 | C2×Dic12 | semidirect |
| 142. C3×C5 | D3×Q16 | semidirect |
| 157. C32 | D5×Q16 | semidirect |
| 170. C5 | D3×Dic12 | semidirect |
| 177. C3 | D5×Dic12 | semidirect |
| 178. C3 | #91264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624219 | 2 |
| C5×#3746 | 2 |
| C3×Dic60 | 2 |
| C3×C8×D15 | 2 |
| #10623826 | 2 |
| #91264 | 3 |
| D5×Dic12 | 3 |
| D3×Dic12 | 5 |