Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
432 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
| 2. C5×#947 | C2 | semidirect |
| 3. C3×#4092 | C2 | semidirect |
| 4. #91469 | C2 | semidirect |
| 5. #91464 | C2 | semidirect |
| 6. #91457 | C2 | semidirect |
| 8. #91435 | C2 | semidirect |
| 9. #91417 | C2 | semidirect |
| 10. #91367 | C2 | semidirect |
| 11. #91357 | C2 | semidirect |
| 38. #4092 | D3 | semidirect |
| 66. #947 | D5 | semidirect |
| 228. C3×C5 | #542 | semidirect |
| 272. C5 | #5643 | semidirect |
| 289. C3 | #66016 | 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×#4092 | 2 |
| #91469 | 2 |
| #91464 | 2 |
| #91457 | 2 |
| #91449 | 2 |
| #91435 | 2 |
| #91417 | 2 |
| #91367 | 2 |
| #91357 | 2 |
| #66016 | 3 |
| #5643 | 5 |