Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
414 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 13. #16840626 | C4 | semidirect |
| 14. #16840625 | C4 | semidirect |
| 17. #16839513 | C4 | semidirect |
| 18. #16839512 | C4 | semidirect |
| 19. C61×#334 | C4 | semidirect |
| 91. C8×C61 | #97 | semidirect |
| 94. #92418 | #97 | semidirect |
| 131. #334 | #6923 | semidirect |
| 132. C61 | #8276 | semidirect |
| 207. C8 | #14519831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461606 | 2 |
| C4×#14519831 | 2 |
| D61⋊#335 | 2 |
| #21460648 | 2 |
| #334×D61 | 2 |
| #8276 | 61 |