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. C3×#4149 | C2 | semidirect |
| 3. C5×#948 | C2 | semidirect |
| 4. #91313 | C2 | semidirect |
| 5. #91312 | C2 | semidirect |
| 6. #91311 | C2 | semidirect |
| 7. C2×#6657 | C2 | semidirect |
| 12. #6817 | C22 | semidirect |
| 13. C2×Dic30 | C22 | semidirect |
| 18. C5×#208 | C22 | semidirect |
| 19. C2×C5×C3⋊C8 | C22 | semidirect |
| 20. #6662 | C22 | semidirect |
| 21. #6658 | C22 | semidirect |
| 22. #6657 | C22 | semidirect |
| 23. #6657 | C22 | semidirect |
| 24. #6653 | C22 | semidirect |
| 27. #4149 | D3 | semidirect |
| 54. #948 | D5 | semidirect |
| 96. #208 | C2×D5 | semidirect |
| 97. C2×C3⋊C8 | C2×D5 | semidirect |
| 167. C3×C5 | #577 | semidirect |
| 201. C5 | #5836 | semidirect |
| 210. C3 | #66085 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #92101 | 2 |
| C3×#4149 | 2 |
| C5×#948 | 2 |
| #91313 | 2 |
| #91312 | 2 |
| #91311 | 2 |
| C2×#6657 | 2 |
| #66085 | 3 |
| #5836 | 5 |