Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
398 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 12. #16840626 | C4 | semidirect |
| 13. #16840625 | C4 | semidirect |
| 17. #16839484 | C4 | semidirect |
| 18. #16839484 | C4 | semidirect |
| 19. #16839483 | C4 | semidirect |
| 20. C61×#322 | C4 | semidirect |
| 91. C8×C61 | #97 | semidirect |
| 95. #92418 | #97 | semidirect |
| 133. #322 | #6923 | semidirect |
| 134. C61 | #8286 | semidirect |
| 209. C8 | #14519831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519845 | 2 |
| #21461613 | 2 |
| D61⋊#335 | 2 |
| #21460654 | 2 |
| #322×D61 | 2 |
| #8286 | 61 |