Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
350 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 8. #16811516 | C4 | semidirect |
| 9. #16811515 | C4 | semidirect |
| 10. #16811514 | C4 | semidirect |
| 11. #16811513 | C4 | semidirect |
| 12. #16811510 | C4 | semidirect |
| 13. C16×#6157 | C4 | semidirect |
| 20. #16810398 | C4 | semidirect |
| 21. C4×#11719908 | C4 | semidirect |
| 22. C16×Dic53 | C4 | semidirect |
| 23. C53×#346 | C4 | semidirect |
| 114. #346 | #6157 | semidirect |
| 121. C53 | #12542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290937 | 2 |
| #20290934 | 2 |
| #20290923 | 2 |
| #20290436 | 2 |
| #20276313 | 2 |
| #12542 | 53 |