Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
284 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 124 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. #91087 | C2 | semidirect |
| 4. C3×#3935 | C2 | semidirect |
| 5. Dic3×#168 | C2 | semidirect |
| 14. #6650 | C4 | semidirect |
| 19. #3935 | D3 | semidirect |
| 28. C3⋊#168 | C2×C4 | semidirect |
| 29. C3×#168 | C2×C4 | semidirect |
| 50. C5×Dic3 | M16 | semidirect |
| 67. #168 | C4×D3 | semidirect |
| 100. C3×C5 | C4×M16 | semidirect |
| 106. Dic3 | #681 | semidirect |
| 123. C5 | #4707 | semidirect |
| 131. C3 | C4×#681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5×D3 | 2 |
| C2×#6650 | 2 |
| #91087 | 2 |
| C3×#3935 | 2 |
| Dic3×#168 | 2 |
| C4×#681 | 3 |
| #4707 | 5 |