Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1132 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20285630 | C2 | semidirect |
| 2. #20285168 | C2 | semidirect |
| 3. #20273798 | C2 | semidirect |
| 4. #20273769 | C2 | semidirect |
| 5. #20273377 | C2 | semidirect |
| 6. #20273132 | C2 | semidirect |
| 7. C53×#3549 | C2 | semidirect |
| 9. C2×#13133214 | C22 | semidirect |
| 13. #16810997 | C22 | semidirect |
| 15. #16810818 | C22 | semidirect |
| 17. #16810676 | C22 | semidirect |
| 18. C4×#11719917 | C22 | semidirect |
| 19. #16810372 | C22 | semidirect |
| 20. #16810367 | C22 | semidirect |
| 21. D4⋊#88322 | C22 | semidirect |
| 24. C53×#555 | C22 | semidirect |
| 26. D42×C53 | C22 | semidirect |
| 174. #3549 | D53 | semidirect |
| 190. #555 | C2×D53 | semidirect |
| 192. D42 | C2×D53 | semidirect |
| 210. C53 | #18714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285630 | 2 |
| #20285168 | 2 |
| #20273798 | 2 |
| #20273769 | 2 |
| #20273377 | 2 |
| #20273132 | 2 |
| C53×#3549 | 2 |
| #18714 | 53 |