Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 13. #16811542 | C4 | semidirect |
| 14. #16811536 | C4 | semidirect |
| 20. #16810731 | C4 | semidirect |
| 21. #16810730 | C4 | semidirect |
| 22. #16810729 | C4 | semidirect |
| 28. C53×#441 | C4 | semidirect |
| 190. #441 | #6157 | semidirect |
| 202. C53 | #12648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#362 | 2 |
| #20291025 | 2 |
| #20290932 | 2 |
| #20290521 | 2 |
| #20289788 | 2 |
| #20289779 | 2 |
| #441×D53 | 2 |
| #12648 | 53 |