Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
406 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 21. #16839484 | C4 | semidirect |
| 22. #16839484 | C4 | semidirect |
| 23. #16839483 | C4 | semidirect |
| 24. C61×#322 | C4 | semidirect |
| 166. #322 | #6923 | semidirect |
| 167. C61 | #8821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461755 | 2 |
| #21461754 | 2 |
| #21461740 | 2 |
| #322×D61 | 2 |
| #8821 | 61 |