Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
304 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C3×C5×Q16 | C2 | semidirect |
| 3. #91835 | C2 | semidirect |
| 4. C2×#6717 | C2 | semidirect |
| 5. #91119 | C2 | semidirect |
| 6. #91105 | C2 | semidirect |
| 7. #91104 | C2 | semidirect |
| 26. C2×C5×Q16 | D3 | semidirect |
| 52. C2×C3×Q16 | D5 | semidirect |
| 122. C2×Q16 | D15 | semidirect |
| 180. C3×C5 | #452 | semidirect |
| 223. C5 | #5187 | semidirect |
| 237. C3 | #65476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6821 | 2 |
| C2×C3×C5×Q16 | 2 |
| #91835 | 2 |
| C2×#6717 | 2 |
| #91119 | 2 |
| #91105 | 2 |
| #91104 | 2 |
| #65476 | 3 |
| #5187 | 5 |