Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 8. C2×C3×C5×C8 | C4 | semidirect |
| 13. #6710 | C4 | semidirect |
| 35. C2×C5×C8 | Dic3 | semidirect |
| 55. C2×C3×C8 | Dic5 | semidirect |
| 104. C2×C8 | Dic15 | semidirect |
| 108. C3×C5 | #344 | semidirect |
| 136. C5 | #4556 | semidirect |
| 146. C3 | #64776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×M16 | 2 |
| #91815 | 2 |
| C2×#6710 | 2 |
| #64776 | 3 |
| #4556 | 5 |