Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 4. #64902 | C3 | direct (N × H) |
| 7. C2×C3×#170 | C4 | semidirect |
| 12. C3×C5×M16 | C4 | semidirect |
| 13. C3×#681 | C4 | semidirect |
| 36. C2×#170 | C3×C4 | semidirect |
| 41. C5×M16 | C3×C4 | semidirect |
| 42. #681 | C3×C4 | semidirect |
| 60. C3×M16 | AGL(1,𝔽5) | semidirect |
| 109. M16 | C3×AGL(1,𝔽5) | semidirect |
| 115. C3×C5 | #344 | semidirect |
| 144. C5 | C3×#344 | semidirect |
| 154. C3 | #64902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4130 | 2 |
| C2×C3×#700 | 2 |
| C3×D5×M16 | 2 |
| #64902 | 3 |
| C3×#344 | 5 |