Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
220 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 68 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. #91233 | C2 | semidirect |
| 3. C3×#4004 | C2 | semidirect |
| 5. #91169 | C2 | semidirect |
| 19. #4004 | D3 | semidirect |
| 125. C3×C5 | #432 | semidirect |
| 158. C5 | #4835 | semidirect |
| 170. C3 | #65684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#1200 | 2 |
| #91233 | 2 |
| C3×#4004 | 2 |
| #91171 | 2 |
| #91169 | 2 |
| #65684 | 3 |
| #4835 | 5 |