Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
216 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 59 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. C3×C4×Dic15 | C2 | semidirect |
| 3. C3×#6710 | C2 | semidirect |
| 8. C5×C4⋊(C3⋊D3) | C4 | semidirect |
| 10. C5×#634 | C4 | semidirect |
| 17. C4×Dic15 | D3 | semidirect |
| 18. #6710 | D3 | semidirect |
| 60. C4⋊(C3⋊D3) | Dic5 | semidirect |
| 62. #634 | Dic5 | semidirect |
| 89. C32×C5 | #104 | semidirect |
| 145. C3×C5 | #805 | semidirect |
| 146. C3×C5 | #825 | semidirect |
| 167. C32 | #3969 | semidirect |
| 184. C5 | #63570 | semidirect |
| 192. C3 | #90978 | semidirect |
| 193. C3 | #90979 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3828 | 2 |
| C3×C4×Dic15 | 2 |
| C3×#6710 | 2 |
| #90979 | 3 |
| #90978 | 3 |
| #63570 | 5 |