Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
220 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 68 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. #91231 | C2 | semidirect |
| 3. C3×#4002 | C2 | semidirect |
| 4. #91177 | C2 | semidirect |
| 21. #4002 | D3 | semidirect |
| 120. C3×C5 | #432 | semidirect |
| 151. C5 | #4705 | semidirect |
| 162. C3 | #65757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D3×Dic5 | 2 |
| #91231 | 2 |
| C3×#4002 | 2 |
| #91177 | 2 |
| (C2×D3)⋊#170 | 2 |
| #65757 | 3 |
| #4705 | 5 |