Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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. C4⋊ΓL(1,𝔽16) | C4 | semidirect |
| 11. C4×ΓL(1,𝔽16) | C4 | semidirect |
| 12. C3×C5×M16 | C4 | semidirect |
| 13. C3×#681 | C4 | semidirect |
| 42. C5×M16 | Dic3 | semidirect |
| 43. #681 | Dic3 | semidirect |
| 61. C3×M16 | AGL(1,𝔽5) | semidirect |
| 113. M16 | ΓL(1,𝔽16) | semidirect |
| 120. C3×C5 | #339 | semidirect |
| 151. C5 | #4555 | semidirect |
| 162. C3 | #64900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91989 | 2 |
| C2×C4×ΓL(1,𝔽16) | 2 |
| C3×D5×M16 | 2 |
| #64900 | 3 |
| #4555 | 5 |