Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1078 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. #20285710 | C2 | semidirect |
| 2. #20285160 | C2 | semidirect |
| 3. #20274021 | C2 | semidirect |
| 4. #20274004 | C2 | semidirect |
| 5. #20273350 | C2 | semidirect |
| 6. #20273326 | C2 | semidirect |
| 7. C53×#3549 | C2 | semidirect |
| 9. #16811173 | C22 | semidirect |
| 10. #16811018 | C22 | semidirect |
| 12. #16811013 | C22 | semidirect |
| 13. #16811013 | C22 | semidirect |
| 15. #16810982 | C22 | semidirect |
| 19. #16810680 | C22 | semidirect |
| 20. C2×#13133128 | C22 | semidirect |
| 21. #16810363 | C22 | semidirect |
| 22. #16810363 | C22 | semidirect |
| 185. #3549 | D53 | semidirect |
| 222. C53 | #19052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285710 | 2 |
| #20285160 | 2 |
| #20274021 | 2 |
| #20274004 | 2 |
| #20273350 | 2 |
| #20273326 | 2 |
| C53×#3549 | 2 |
| #19052 | 53 |