Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
516 conjugacy classes of subgroups; only the 374 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 374 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. C3×#4094 | C2 | semidirect |
| 3. C2×C3×#681 | C2 | semidirect |
| 4. #66153 | C3 | direct (N × H) |
| 11. C3×#681 | C22 | semidirect |
| 12. C2×C3×#168 | C22 | semidirect |
| 15. #4094 | C2×C3 | semidirect |
| 16. C2×#681 | C2×C3 | semidirect |
| 34. #681 | C22×C3 | semidirect |
| 35. C2×#168 | C22×C3 | semidirect |
| 87. C3×C5 | #568 | semidirect |
| 108. C5 | C3×#568 | semidirect |
| 115. C3 | #66153 | 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×#41 | 2 |
| C3×#4094 | 2 |
| C2×C3×#681 | 2 |
| #66153 | 3 |
| C3×#568 | 5 |