Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
252 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 88 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. #91177 | C2 | semidirect |
| 5. Dic3⋊#170 | C2 | semidirect |
| 59. Dic15 | M16 | semidirect |
| 64. C5×Dic3 | M16 | semidirect |
| 133. C3×C5 | #423 | semidirect |
| 144. Dic3 | #704 | semidirect |
| 166. C5 | #5118 | semidirect |
| 178. C3 | #65758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6762 | 2 |
| C2×C3×#704 | 2 |
| C2×Dic3×Dic5 | 2 |
| #91177 | 2 |
| Dic3⋊#170 | 2 |
| #65758 | 3 |
| #5118 | 5 |