Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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. #20285453 | C2 | semidirect |
| 2. #20276929 | C2 | semidirect |
| 3. #20276886 | C2 | semidirect |
| 4. #20276791 | C2 | semidirect |
| 5. #20276661 | C2 | semidirect |
| 6. #20276613 | C2 | semidirect |
| 7. #20276527 | C2 | semidirect |
| 8. C53×#2956 | C2 | semidirect |
| 11. #16811021 | C22 | semidirect |
| 12. #16811000 | C22 | semidirect |
| 17. #16810736 | C22 | semidirect |
| 18. #16810447 | C22 | semidirect |
| 19. #16810444 | C22 | semidirect |
| 20. #16810435 | C22 | semidirect |
| 23. #16810401 | C22 | semidirect |
| 89. Q16×C53 | #41 | semidirect |
| 93. D8×C53 | #41 | semidirect |
| 166. #2956 | D53 | semidirect |
| 202. C53 | #33688 | semidirect |
| 259. Q16 | #11719945 | semidirect |
| 265. D8 | #11719945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285453 | 2 |
| #20276929 | 2 |
| #20276886 | 2 |
| #20276791 | 2 |
| #20276661 | 2 |
| #20276613 | 2 |
| #20276527 | 2 |
| C53×#2956 | 2 |
| #33688 | 53 |