Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
296 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 3. C2×#6663 | C2 | semidirect |
| 5. #90975 | C2 | semidirect |
| 56. C22×C3×C5 | Q16 | semidirect |
| 111. C22×C5 | Dic12 | semidirect |
| 129. C3×C5 | #451 | semidirect |
| 132. C22×C3 | #689 | semidirect |
| 160. C5 | #4739 | semidirect |
| 163. C22 | #6663 | semidirect |
| 170. C3 | #65339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic30 | 2 |
| C5×#924 | 2 |
| C2×#6663 | 2 |
| C3×C22⋊#168 | 2 |
| #90975 | 2 |
| #65339 | 3 |
| #4739 | 5 |