Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
310 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 13. C3×C5×Dic6 | C4 | semidirect |
| 29. C3⋊Dic15 | Q8 | semidirect |
| 51. C5×Dic6 | Dic3 | semidirect |
| 68. C3×Dic6 | Dic5 | semidirect |
| 96. C32×C5 | C4×Q8 | semidirect |
| 133. Dic6 | Dic15 | semidirect |
| 149. C3×C5 | #887 | semidirect |
| 150. C3×C5 | Q8×Dic3 | semidirect |
| 170. C32 | Q8×Dic5 | semidirect |
| 186. C5 | #63843 | semidirect |
| 194. C3 | #91344 | semidirect |
| 195. C3 | Q8×Dic15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Dic6 | 2 |
| C4×C3⋊Dic15 | 2 |
| C3×C4⋊Dic15 | 2 |
| Dic3⋊Dic15 | 2 |
| Dic3×Dic15 | 2 |
| Q8×Dic15 | 3 |
| #91344 | 3 |
| #63843 | 5 |