Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1328 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 251 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. #20289427 | C2 | semidirect |
| 3. #20283412 | C2 | semidirect |
| 4. #20275131 | C2 | semidirect |
| 5. #20275000 | C2 | semidirect |
| 6. #20274518 | C2 | semidirect |
| 7. C53×#1791 | C2 | semidirect |
| 12. C22×C8×D53 | C22 | semidirect |
| 18. #16810649 | C22 | semidirect |
| 20. #16810586 | C22 | semidirect |
| 21. #16810581 | C22 | semidirect |
| 22. #16810395 | C22 | semidirect |
| 34. C2×#11719917 | D4 | semidirect |
| 37. C22×#88322 | D4 | semidirect |
| 146. #1791 | D53 | semidirect |
| 170. C53 | #21483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289427 | 2 |
| #20284107 | 2 |
| #20283412 | 2 |
| #20275131 | 2 |
| #20275000 | 2 |
| #20274518 | 2 |
| C53×#1791 | 2 |
| #21483 | 53 |