Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
370 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 17. #16839515 | C4 | semidirect |
| 18. #16839514 | C4 | semidirect |
| 19. C61×#335 | C4 | semidirect |
| 100. C8×C61 | #107 | semidirect |
| 103. #92418 | #107 | semidirect |
| 144. #335 | #6923 | semidirect |
| 145. C61 | #9617 | semidirect |
| 229. C8 | #14519846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461930 | 2 |
| #21461754 | 2 |
| #21461613 | 2 |
| #21460698 | 2 |
| #335×D61 | 2 |
| #9617 | 61 |