Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
304 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 72 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×#6716 | C2 | semidirect |
| 3. #91365 | C2 | semidirect |
| 4. C2×#6663 | C2 | semidirect |
| 5. C3×#3964 | C2 | semidirect |
| 6. #90972 | C2 | semidirect |
| 7. (C2×D3)⋊#168 | C2 | semidirect |
| 30. #3964 | D3 | semidirect |
| 180. C3×C5 | #452 | semidirect |
| 223. C5 | #4783 | semidirect |
| 237. C3 | #65528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#237 | 2 |
| C2×#6716 | 2 |
| #91365 | 2 |
| C2×#6663 | 2 |
| C3×#3964 | 2 |
| #90972 | 2 |
| (C2×D3)⋊#168 | 2 |
| #65528 | 3 |
| #4783 | 5 |