Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
532 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 200 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×Q8×Dic3 | C2 | semidirect |
| 3. C3×Q8×Dic5 | C2 | semidirect |
| 6. #91340 | C2 | semidirect |
| 7. #91333 | C2 | semidirect |
| 10. Q8×D15 | C4 | semidirect |
| 25. Q8×Dic5 | D3 | semidirect |
| 42. Q8×Dic3 | D5 | semidirect |
| 138. C3×C5 | #519 | semidirect |
| 167. C5 | #5572 | semidirect |
| 178. C3 | #65906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D15 | 2 |
| C5×Q8×Dic3 | 2 |
| C3×Q8×Dic5 | 2 |
| #91386 | 2 |
| #91347 | 2 |
| #91340 | 2 |
| #91333 | 2 |
| #65906 | 3 |
| #5572 | 5 |