Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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×#6705 | C2 | semidirect |
| 3. C2×C8×D15 | C2 | semidirect |
| 4. C3×C5×C22⋊C8 | C2 | semidirect |
| 5. #91114 | C2 | semidirect |
| 6. #91104 | C2 | semidirect |
| 7. #91104 | C2 | semidirect |
| 28. C5×C22⋊C8 | D3 | semidirect |
| 56. C3×C22⋊C8 | D5 | semidirect |
| 133. C22⋊C8 | D15 | semidirect |
| 191. C3×C5 | #408 | semidirect |
| 240. C5 | #4727 | semidirect |
| 256. C3 | #65016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6817 | 2 |
| C2×#6705 | 2 |
| C2×C8×D15 | 2 |
| C3×C5×C22⋊C8 | 2 |
| #91114 | 2 |
| #91104 | 2 |
| #65016 | 3 |
| #4727 | 5 |