Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 75 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. #91790 | C2 | semidirect |
| 3. C3×C4×C5×C8 | C2 | semidirect |
| 4. #91103 | C2 | semidirect |
| 5. #91089 | C2 | semidirect |
| 12. Dic60 | C4 | semidirect |
| 13. D120 | C4 | semidirect |
| 14. #6706 | C4 | semidirect |
| 20. C4×C5×C8 | D3 | semidirect |
| 36. C3×C4×C8 | D5 | semidirect |
| 81. C4×C8 | D15 | semidirect |
| 112. C3×C5 | #443 | semidirect |
| 136. C5 | #4700 | semidirect |
| 143. C3 | #64989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91793 | 2 |
| #91790 | 2 |
| C3×C4×C5×C8 | 2 |
| #91103 | 2 |
| #91089 | 2 |
| #64989 | 3 |
| #4700 | 5 |