Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 7. #6762 | C4 | semidirect |
| 12. C2×C3×C5×C8 | C4 | semidirect |
| 13. C2×C3×#168 | C4 | semidirect |
| 41. C2×C5×C8 | Dic3 | semidirect |
| 42. C2×#168 | Dic3 | semidirect |
| 59. C2×C3×C8 | AGL(1,𝔽5) | semidirect |
| 111. C2×C8 | ΓL(1,𝔽16) | semidirect |
| 115. C3×C5 | #344 | semidirect |
| 144. C5 | #4556 | semidirect |
| 154. C3 | #64894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91989 | 2 |
| D5⋊#208 | 2 |
| C2×C3×#676 | 2 |
| #64894 | 3 |
| #4556 | 5 |