Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
164 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 47 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. Q16×D15 | C2 | semidirect |
| 3. C3×C5×Q32 | C2 | semidirect |
| 4. #91113 | C2 | semidirect |
| 5. #91112 | C2 | semidirect |
| 6. #91084 | C2 | semidirect |
| 7. #91082 | C2 | semidirect |
| 23. C5×Q32 | D3 | semidirect |
| 41. C3×Q32 | D5 | semidirect |
| 90. Q32 | D15 | semidirect |
| 126. C3×C5 | #510 | semidirect |
| 151. C5 | #4918 | semidirect |
| 159. C3 | #65207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91808 | 2 |
| Q16×D15 | 2 |
| C3×C5×Q32 | 2 |
| #91113 | 2 |
| #91112 | 2 |
| #91084 | 2 |
| #91082 | 2 |
| #65207 | 3 |
| #4918 | 5 |