Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
192 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 67 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. #91759 | C2 | semidirect |
| 3. C3×C4×C5×C8 | C2 | semidirect |
| 5. #91100 | C2 | semidirect |
| 17. C4×C5×C8 | D3 | semidirect |
| 30. C3×C4×C8 | D5 | semidirect |
| 67. C4×C8 | D15 | semidirect |
| 93. C3×C5 | #488 | semidirect |
| 115. C5 | #4697 | semidirect |
| 123. C3 | #64986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91764 | 2 |
| #91759 | 2 |
| C3×C4×C5×C8 | 2 |
| #91105 | 2 |
| #91100 | 2 |
| #64986 | 3 |
| #4697 | 5 |