Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 228 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 |
|---|---|---|
| 3. #91223 | C2 | semidirect |
| 4. C3×#3994 | C2 | semidirect |
| 5. #91159 | C2 | semidirect |
| 12. C8×D15 | C4 | semidirect |
| 13. C5×D3×C8 | C4 | semidirect |
| 15. #6648 | C4 | semidirect |
| 16. D3×#168 | C4 | semidirect |
| 22. #3994 | D3 | semidirect |
| 75. D3×C8 | AGL(1,𝔽5) | semidirect |
| 134. C3×C5 | #427 | semidirect |
| 169. C5 | #4880 | semidirect |
| 181. C3 | #65721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91907 | 2 |
| D3×C8×D5 | 2 |
| #91223 | 2 |
| C3×#3994 | 2 |
| #91159 | 2 |
| #65721 | 3 |
| #4880 | 5 |