Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
418 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 31. #14519688 | C8 | semidirect |
| 84. #92418 | C4⋊C8 | semidirect |
| 121. C61 | #8808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461751 | 2 |
| #21461734 | 2 |
| C2×#16840626 | 2 |
| C2×#16840624 | 2 |
| #97×Dic61 | 2 |
| #8808 | 61 |