Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 101 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. Q8×Dic15 | C2 | semidirect |
| 4. #91119 | C2 | semidirect |
| 6. #91102 | C2 | semidirect |
| 7. #91099 | C2 | semidirect |
| 12. C3×C5×SD16 | C4 | semidirect |
| 31. C3×C5×Q8 | C2×C4 | semidirect |
| 41. C3×C5×C8 | C2×C4 | semidirect |
| 53. C5×SD16 | Dic3 | semidirect |
| 77. C3×SD16 | Dic5 | semidirect |
| 88. C5×Q8 | C2×Dic3 | semidirect |
| 98. C5×C8 | C2×Dic3 | semidirect |
| 113. C3×Q8 | C2×Dic5 | semidirect |
| 123. C3×C8 | C2×Dic5 | semidirect |
| 139. SD16 | Dic15 | semidirect |
| 148. C3×C5 | #440 | semidirect |
| 166. Q8 | C2×Dic15 | semidirect |
| 177. C8 | C2×Dic15 | semidirect |
| 182. C5 | #5164 | semidirect |
| 194. C3 | #65453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×SD16 | 2 |
| Q8×Dic15 | 2 |
| D4×Dic15 | 2 |
| #91119 | 2 |
| #91116 | 2 |
| #91102 | 2 |
| #91099 | 2 |
| #65453 | 3 |
| #5164 | 5 |