Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C22×C3×C5×C8 | C2 | semidirect |
| 3. #91815 | C2 | semidirect |
| 4. #91105 | C2 | semidirect |
| 5. #91100 | C2 | semidirect |
| 10. #6817 | C4 | semidirect |
| 21. C22×C5×C8 | D3 | semidirect |
| 41. C22×C3×C8 | D5 | semidirect |
| 96. C22×C8 | D15 | semidirect |
| 141. C3×C5 | #416 | semidirect |
| 175. C5 | #5113 | semidirect |
| 186. C3 | #65402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6817 | 2 |
| C22×C3×C5×C8 | 2 |
| #91815 | 2 |
| #91105 | 2 |
| #91100 | 2 |
| #65402 | 3 |
| #5113 | 5 |