Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
564 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20285448 | C2 | semidirect |
| 2. #20283625 | C2 | semidirect |
| 3. #20276930 | C2 | semidirect |
| 4. #20276927 | C2 | semidirect |
| 5. #20276884 | C2 | semidirect |
| 6. #20276789 | C2 | semidirect |
| 7. #20276661 | C2 | semidirect |
| 8. #20276614 | C2 | semidirect |
| 9. #20276610 | C2 | semidirect |
| 10. #20276524 | C2 | semidirect |
| 11. C53×#2190 | C2 | semidirect |
| 15. #16811020 | C22 | semidirect |
| 16. #16810998 | C22 | semidirect |
| 24. #16810735 | C22 | semidirect |
| 25. #16810734 | C22 | semidirect |
| 30. #16810446 | C22 | semidirect |
| 31. #16810445 | C22 | semidirect |
| 32. #16810443 | C22 | semidirect |
| 33. #16810437 | C22 | semidirect |
| 34. #16810436 | C22 | semidirect |
| 37. #16810400 | C22 | semidirect |
| 111. Q16×C53 | #41 | semidirect |
| 116. D8×C53 | #41 | semidirect |
| 209. #2190 | D53 | semidirect |
| 250. C53 | #33688 | semidirect |
| 319. Q16 | #11719947 | semidirect |
| 326. D8 | #11719947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285448 | 2 |
| #20283625 | 2 |
| #20276930 | 2 |
| #20276927 | 2 |
| #20276884 | 2 |
| #20276789 | 2 |
| #20276661 | 2 |
| #20276614 | 2 |
| #20276610 | 2 |
| #20276524 | 2 |
| C53×#2190 | 2 |
| #33688 | 53 |