Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
284 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 64 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. #91833 | C2 | semidirect |
| 3. #91322 | C2 | semidirect |
| 4. C3×#3968 | C2 | semidirect |
| 5. #90978 | C2 | semidirect |
| 23. #3968 | D3 | semidirect |
| 127. C3×C5 | #456 | semidirect |
| 155. C5 | #4752 | semidirect |
| 163. C3 | #65535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1007 | 2 |
| #91833 | 2 |
| #91322 | 2 |
| C3×#3968 | 2 |
| #90978 | 2 |
| #65535 | 3 |
| #4752 | 5 |