Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
660 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 243 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 |
|---|---|---|
| 4. C2×#6712 | C2 | semidirect |
| 5. C2×C4×Dic15 | C2 | semidirect |
| 6. #91766 | C2 | direct (N × H) |
| 10. C22×Dic15 | C4 | semidirect |
| 17. #6712 | C22 | semidirect |
| 18. C4×Dic15 | C22 | semidirect |
| 35. C2×Dic15 | C2×C4 | semidirect |
| 98. C2×C3×C5 | #117 | semidirect |
| 135. C3×C5 | C2×#117 | semidirect |
| 147. C2×C5 | #877 | semidirect |
| 164. C2×C3 | #4023 | semidirect |
| 167. C5 | C2×#877 | semidirect |
| 178. C3 | C2×#4023 | semidirect |
| 180. C2 | #91766 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic15 | 2 |
| C2×C3×C5×C22⋊C4 | 2 |
| C2×#6719 | 2 |
| C2×#6712 | 2 |
| C2×C4×Dic15 | 2 |
| #91766 | 2 |
| C2×#4023 | 3 |
| C2×#877 | 5 |