Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
274 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 7. #16840651 | C4 | semidirect |
| 12. #16839513 | C4 | semidirect |
| 14. C61×#334 | C4 | semidirect |
| 20. #14519846 | C8 | semidirect |
| 109. #334 | #6923 | semidirect |
| 110. C61 | #7178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462020 | 2 |
| C4×#14519846 | 2 |
| #334×D61 | 2 |
| #7178 | 61 |