Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
526 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 118 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. #21461740 | C2 | semidirect |
| 3. D61⋊#334 | C2 | semidirect |
| 4. #21460698 | C2 | semidirect |
| 16. C8×D244 | C4 | semidirect |
| 17. D4×#92418 | C4 | semidirect |
| 18. #16839827 | C4 | semidirect |
| 24. C8×D4×C61 | C4 | semidirect |
| 198. C8×D4 | #6923 | semidirect |
| 210. C61 | #8646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461740 | 2 |
| #21461687 | 2 |
| D61⋊#334 | 2 |
| #21460698 | 2 |
| C8×D4×D61 | 2 |
| #8646 | 61 |