Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
516 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 152 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. #92101 | C2 | semidirect |
| 2. C5×#1009 | C2 | semidirect |
| 3. C3×#4094 | C2 | semidirect |
| 4. #91322 | C2 | semidirect |
| 5. C2×#6659 | C2 | semidirect |
| 6. #91304 | C2 | semidirect |
| 7. #91303 | C2 | semidirect |
| 12. #6817 | C22 | semidirect |
| 13. C2×Dic30 | C22 | semidirect |
| 18. C3×#681 | C22 | semidirect |
| 19. C2×C3×#168 | C22 | semidirect |
| 20. #6663 | C22 | semidirect |
| 21. #6660 | C22 | semidirect |
| 22. #6659 | C22 | semidirect |
| 23. #6659 | C22 | semidirect |
| 24. #6654 | C22 | semidirect |
| 30. #4094 | D3 | semidirect |
| 51. #1009 | D5 | semidirect |
| 71. #681 | C2×D3 | semidirect |
| 72. C2×#168 | C2×D3 | semidirect |
| 167. C3×C5 | #577 | semidirect |
| 201. C5 | #5751 | semidirect |
| 210. C3 | #66170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #92101 | 2 |
| C5×#1009 | 2 |
| C3×#4094 | 2 |
| #91322 | 2 |
| C2×#6659 | 2 |
| #91304 | 2 |
| #91303 | 2 |
| #66170 | 3 |
| #5751 | 5 |