Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
220 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. C2×C3×Dic20 | C2 | semidirect |
| 4. C3×#3949 | C2 | semidirect |
| 5. C3×#3948 | C2 | semidirect |
| 6. #65426 | C3 | direct (N × H) |
| 19. C2×Dic20 | C2×C3 | semidirect |
| 20. #3949 | C2×C3 | semidirect |
| 21. #3948 | C2×C3 | semidirect |
| 112. C3×C5 | #470 | semidirect |
| 138. C5 | C3×#470 | semidirect |
| 147. C3 | #65426 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×M16 | 2 |
| C3×#4070 | 2 |
| C2×C3×Dic20 | 2 |
| C3×#3949 | 2 |
| C3×#3948 | 2 |
| #65426 | 3 |
| C3×#470 | 5 |