Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
712 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#16811064 | C2 | semidirect |
| 3. #20283583 | C2 | semidirect |
| 4. #20276775 | C2 | semidirect |
| 5. #20276753 | C2 | semidirect |
| 6. #20276473 | C2 | semidirect |
| 7. #20276431 | C2 | semidirect |
| 8. #20276423 | C2 | semidirect |
| 9. C22×SD32×C53 | C2 | semidirect |
| 15. C2×#13133163 | C22 | semidirect |
| 16. C2×#13133160 | C22 | semidirect |
| 22. Q16×Dic53 | C22 | semidirect |
| 26. #16810441 | C22 | semidirect |
| 27. #16810428 | C22 | semidirect |
| 28. #16810425 | C22 | semidirect |
| 67. C2×Q16×C53 | D4 | semidirect |
| 173. C22×SD32 | D53 | semidirect |
| 211. C53 | #33587 | semidirect |
| 221. C2×Q16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| #20285196 | 2 |
| #20283583 | 2 |
| #20276775 | 2 |
| #20276753 | 2 |
| #20276473 | 2 |
| #20276431 | 2 |
| #20276423 | 2 |
| C22×SD32×C53 | 2 |
| #33587 | 53 |