Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
236 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 89 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. #91223 | C2 | semidirect |
| 5. #91222 | C2 | semidirect |
| 15. C3×C5×M16 | C4 | semidirect |
| 16. C3×#681 | C4 | semidirect |
| 17. C3×#676 | C4 | semidirect |
| 36. C3×C5×C8 | C2×C4 | semidirect |
| 37. C3×#168 | C2×C4 | semidirect |
| 51. C5×M16 | Dic3 | semidirect |
| 52. #681 | Dic3 | semidirect |
| 53. #676 | Dic3 | semidirect |
| 72. C3×M16 | AGL(1,𝔽5) | semidirect |
| 91. C5×C8 | C2×Dic3 | semidirect |
| 92. #168 | C2×Dic3 | semidirect |
| 115. C3×C8 | C2×AGL(1,𝔽5) | semidirect |
| 132. M16 | ΓL(1,𝔽16) | semidirect |
| 140. C3×C5 | #428 | semidirect |
| 170. C8 | C2×ΓL(1,𝔽16) | semidirect |
| 176. C5 | #5121 | semidirect |
| 189. C3 | #65727 | 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 |
| #91223 | 2 |
| #91222 | 2 |
| #65727 | 3 |
| #5121 | 5 |