Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
416 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 60 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. #21462092 | C2 | semidirect |
| 2. #21460952 | C2 | semidirect |
| 3. #21460950 | C2 | semidirect |
| 11. #16840141 | C4 | semidirect |
| 14. #16840134 | C4 | semidirect |
| 15. C2×C4×#92418 | C4 | semidirect |
| 16. C61×#532 | C4 | semidirect |
| 131. #532 | #6923 | semidirect |
| 141. C61 | #13583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462092 | 2 |
| #21460952 | 2 |
| #21460950 | 2 |
| #21456245 | 2 |
| #13583 | 61 |