Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
424 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 1. Q8×Dic15 | C2 | semidirect |
| 3. C3×#4090 | C2 | semidirect |
| 4. C4×#1204 | C2 | semidirect |
| 5. #91417 | C2 | semidirect |
| 7. #91400 | C2 | semidirect |
| 9. #91367 | C2 | semidirect |
| 10. #91342 | C2 | semidirect |
| 11. Dic3×Dic10 | C2 | semidirect |
| 39. #4090 | D3 | semidirect |
| 220. C3×C5 | #556 | semidirect |
| 259. C5 | #5732 | semidirect |
| 274. C3 | #66005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic15 | 2 |
| C5×#947 | 2 |
| C3×#4090 | 2 |
| C4×#1204 | 2 |
| #91417 | 2 |
| Dic5×D12 | 2 |
| #91400 | 2 |
| #91370 | 2 |
| #91367 | 2 |
| #91342 | 2 |
| Dic3×Dic10 | 2 |
| #66005 | 3 |
| #5732 | 5 |