Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
452 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. #21461574 | C2 | semidirect |
| 4. #21460920 | C2 | semidirect |
| 9. #16840672 | C4 | semidirect |
| 10. #16840670 | C4 | semidirect |
| 18. #16839785 | C4 | semidirect |
| 20. #16839729 | C4 | semidirect |
| 21. C2×#14519687 | C4 | semidirect |
| 22. C2×#131×C61 | C4 | semidirect |
| 153. C2×#131 | #6923 | semidirect |
| 169. C61 | #12634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462110 | 2 |
| #21462090 | 2 |
| #21461574 | 2 |
| #21460920 | 2 |
| #21454535 | 2 |
| #12634 | 61 |