Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 228 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 |
|---|---|---|
| 4. C2×#6663 | C2 | semidirect |
| 5. #90988 | C2 | semidirect |
| 6. #90975 | C2 | semidirect |
| 7. #90973 | C2 | semidirect |
| 68. C22×C3×C5 | Q16 | semidirect |
| 133. C22×C5 | Dic12 | semidirect |
| 155. C3×C5 | #467 | semidirect |
| 158. C22×C3 | #689 | semidirect |
| 190. C5 | #5116 | semidirect |
| 193. C22 | #6663 | semidirect |
| 202. C3 | #65340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91813 | 2 |
| C5×#924 | 2 |
| C22×C3×#168 | 2 |
| C2×#6663 | 2 |
| #90988 | 2 |
| #90975 | 2 |
| #90973 | 2 |
| #65340 | 3 |
| #5116 | 5 |