Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
308 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. C2×C3×C5×M16 | C2 | semidirect |
| 3. #91815 | C2 | semidirect |
| 4. #91109 | C2 | semidirect |
| 10. #6817 | C4 | semidirect |
| 12. C2×D60 | C4 | semidirect |
| 14. C2×Dic30 | C4 | semidirect |
| 16. C3×C5×M16 | C22 | semidirect |
| 20. C4×Dic15 | C22 | semidirect |
| 23. C2×C5×M16 | D3 | semidirect |
| 46. C2×C3×M16 | D5 | semidirect |
| 59. C5×M16 | C2×D3 | semidirect |
| 87. C3×M16 | C2×D5 | semidirect |
| 112. C2×M16 | D15 | semidirect |
| 161. M16 | C2×D15 | semidirect |
| 166. C3×C5 | #421 | semidirect |
| 208. C5 | #5139 | semidirect |
| 221. C3 | #65428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6817 | 2 |
| C2×C3×C5×M16 | 2 |
| #91815 | 2 |
| #91109 | 2 |
| #65428 | 3 |
| #5139 | 5 |