Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
292 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 63 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×C5×AGL(1,ℤ/8) | C2 | semidirect |
| 3. #91825 | C2 | semidirect |
| 4. #91821 | C2 | semidirect |
| 5. #91121 | C2 | semidirect |
| 6. #91109 | C2 | semidirect |
| 7. #91108 | C2 | semidirect |
| 28. C5×AGL(1,ℤ/8) | D3 | semidirect |
| 57. C3×AGL(1,ℤ/8) | D5 | semidirect |
| 133. AGL(1,ℤ/8) | D15 | semidirect |
| 193. C3×C5 | #454 | semidirect |
| 237. C5 | #5201 | semidirect |
| 249. C3 | #65490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #92101 | 2 |
| C3×C5×AGL(1,ℤ/8) | 2 |
| #91825 | 2 |
| #91821 | 2 |
| #91121 | 2 |
| #91109 | 2 |
| #91108 | 2 |
| #65490 | 3 |
| #5201 | 5 |