Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
526 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 14. #16840167 | C4 | semidirect |
| 16. #16840165 | C4 | semidirect |
| 19. C61×#500 | C4 | semidirect |
| 105. C8×C61 | #103 | semidirect |
| 106. #92418 | #103 | semidirect |
| 140. #500 | #6923 | semidirect |
| 150. C61 | #9823 | semidirect |
| 237. C8 | #14519840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462000 | 2 |
| #21461946 | 2 |
| #21461755 | 2 |
| C8×D61⋊C8 | 2 |
| #500×D61 | 2 |
| #9823 | 61 |