Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C2×#6740 | C2 | semidirect |
| 2. C2×#6739 | C2 | semidirect |
| 4. #91233 | C2 | semidirect |
| 5. C3×C4×#170 | C2 | semidirect |
| 6. #91171 | C2 | semidirect |
| 7. (C2×D3)⋊#170 | C2 | semidirect |
| 29. C4×#170 | D3 | semidirect |
| 45. C3×#170 | D4 | semidirect |
| 76. C3×Dic5 | M16 | semidirect |
| 108. #170 | D12 | semidirect |
| 147. Dic5 | ΓL(1,𝔽25) | semidirect |
| 163. C3×C5 | #436 | semidirect |
| 203. C5 | #4688 | semidirect |
| 217. C3 | #65695 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6740 | 2 |
| C2×#6739 | 2 |
| #91405 | 2 |
| #91233 | 2 |
| C3×C4×#170 | 2 |
| #91171 | 2 |
| (C2×D3)⋊#170 | 2 |
| #65695 | 3 |
| #4688 | 5 |