Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
274 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 9. #16840684 | C4 | semidirect |
| 14. C8×#92418 | C4 | semidirect |
| 15. C82×C61 | C4 | semidirect |
| 21. #14519848 | C8 | semidirect |
| 23. #14519846 | C8 | semidirect |
| 117. C82 | #6923 | semidirect |
| 118. C61 | #7179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#364 | 2 |
| #21461621 | 2 |
| C82×D61 | 2 |
| #7179 | 61 |