Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 66 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. #10624197 | C2 | semidirect |
| 2. #10623901 | C2 | semidirect |
| 3. C3×Dic60 | C2 | semidirect |
| 4. C3×C5×D3×C8 | C2 | semidirect |
| 5. #10623804 | C2 | semidirect |
| 19. Dic60 | D3 | semidirect |
| 24. C5×D3×C8 | D3 | semidirect |
| 36. C3×D3×C8 | D5 | semidirect |
| 93. D3×C8 | D15 | semidirect |
| 94. C32×C5 | #135 | semidirect |
| 146. C3×C5 | #904 | semidirect |
| 147. C3×C5 | #919 | semidirect |
| 163. C32 | #4050 | semidirect |
| 179. C5 | #63808 | semidirect |
| 186. C3 | #91275 | semidirect |
| 187. C3 | #91793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624197 | 2 |
| #10623901 | 2 |
| C3×Dic60 | 2 |
| C3×C5×D3×C8 | 2 |
| #10623804 | 2 |
| #91793 | 3 |
| #91275 | 3 |
| #63808 | 5 |