Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 4. #90990 | C2 | semidirect |
| 5. #90987 | C2 | semidirect |
| 6. #90971 | C2 | semidirect |
| 7. #90971 | C2 | semidirect |
| 141. C3×C5 | #485 | semidirect |
| 174. C5 | #5045 | semidirect |
| 186. C3 | #65012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91815 | 2 |
| C3×#4070 | 2 |
| C5×#830 | 2 |
| #90990 | 2 |
| #90987 | 2 |
| #90971 | 2 |
| #65012 | 3 |
| #5045 | 5 |