Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
902 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 902 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20284221 | C2 | semidirect |
| 2. #20284087 | C2 | semidirect |
| 3. #20276268 | C2 | semidirect |
| 4. #20276169 | C2 | semidirect |
| 5. #20275989 | C2 | semidirect |
| 6. #20275824 | C2 | semidirect |
| 7. #20275244 | C2 | semidirect |
| 8. #20275205 | C2 | semidirect |
| 9. C53×#1794 | C2 | semidirect |
| 12. C22×D424 | C22 | semidirect |
| 14. #16811097 | C22 | semidirect |
| 19. #16810672 | C22 | semidirect |
| 20. #16810649 | C22 | semidirect |
| 23. #16810627 | C22 | semidirect |
| 25. C2×#13133133 | C22 | semidirect |
| 26. #16810393 | C22 | semidirect |
| 27. #16810388 | C22 | semidirect |
| 28. #16810380 | C22 | semidirect |
| 29. #16810379 | C22 | semidirect |
| 48. #13133213 | D4 | semidirect |
| 49. #13133206 | D4 | semidirect |
| 213. #1794 | D53 | semidirect |
| 245. C53 | #30441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284221 | 2 |
| #20284087 | 2 |
| #20276268 | 2 |
| #20276169 | 2 |
| #20275989 | 2 |
| #20275824 | 2 |
| #20275244 | 2 |
| #20275205 | 2 |
| C53×#1794 | 2 |
| #30441 | 53 |