Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
486 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 16. #16840167 | C4 | semidirect |
| 19. #16840165 | C4 | semidirect |
| 23. C61×#500 | C4 | semidirect |
| 120. C8×C61 | #103 | semidirect |
| 122. #92418 | #103 | semidirect |
| 156. #500 | #6923 | semidirect |
| 169. C61 | #9731 | semidirect |
| 268. C8 | #14519840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461985 | 2 |
| C8×C4⋊#6923 | 2 |
| D61⋊#335 | 2 |
| D61⋊#332 | 2 |
| #500×D61 | 2 |
| #9731 | 61 |