Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
532 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 240 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. Q8×Dic15 | C2 | semidirect |
| 3. C3×Q8×Dic5 | C2 | semidirect |
| 5. #91344 | C2 | semidirect |
| 7. Dic5×Dic6 | C2 | semidirect |
| 10. C5×D3×Q8 | C4 | semidirect |
| 27. Q8×Dic5 | D3 | semidirect |
| 72. D3×Q8 | Dic5 | semidirect |
| 138. C3×C5 | #519 | semidirect |
| 167. C5 | #5572 | semidirect |
| 178. C3 | #66146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×Q8 | 2 |
| Q8×Dic15 | 2 |
| C3×Q8×Dic5 | 2 |
| #91371 | 2 |
| #91344 | 2 |
| #91338 | 2 |
| Dic5×Dic6 | 2 |
| #66146 | 3 |
| #5572 | 5 |