Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 76 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. #91813 | C2 | semidirect |
| 3. C22×C3×#168 | C2 | semidirect |
| 4. C2×#6659 | C2 | semidirect |
| 5. #90985 | C2 | semidirect |
| 6. #90975 | C2 | semidirect |
| 7. #90967 | C2 | semidirect |
| 26. C22×#168 | D3 | semidirect |
| 45. C3×#168 | D4 | semidirect |
| 69. C22×C3×C5 | SD16 | semidirect |
| 108. #168 | #67 | semidirect |
| 142. C22×C5 | #204 | semidirect |
| 163. C3×C5 | #465 | semidirect |
| 166. C22×C3 | #687 | semidirect |
| 203. C5 | #5114 | semidirect |
| 209. C22 | #6659 | semidirect |
| 217. C3 | #65330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91813 | 2 |
| C5×#930 | 2 |
| C22×C3×#168 | 2 |
| C2×#6659 | 2 |
| #90985 | 2 |
| #90975 | 2 |
| #90967 | 2 |
| #65330 | 3 |
| #5114 | 5 |