Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
470 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 90 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. #21462788 | C2 | semidirect |
| 2. #21462141 | C2 | semidirect |
| 3. #21461702 | C2 | semidirect |
| 4. #21460892 | C2 | semidirect |
| 17. #16840017 | C4 | semidirect |
| 18. #16840016 | C4 | semidirect |
| 19. #16840015 | C4 | semidirect |
| 24. C61×#470 | C4 | semidirect |
| 27. #14519852 | D4 | semidirect |
| 191. #470 | #6923 | semidirect |
| 202. C61 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462788 | 2 |
| #21462141 | 2 |
| #21461702 | 2 |
| #21460892 | 2 |
| #21455483 | 2 |
| #13077 | 61 |