Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
258 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 9. #16811512 | C4 | semidirect |
| 10. #16811511 | C4 | semidirect |
| 11. #16811509 | C4 | semidirect |
| 12. C4×#11719910 | C4 | semidirect |
| 18. #16810401 | C4 | semidirect |
| 19. #16810400 | C4 | semidirect |
| 20. C53×#347 | C4 | semidirect |
| 105. #347 | #6157 | semidirect |
| 113. C53 | #12597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290925 | 2 |
| #20290437 | 2 |
| #20289771 | 2 |
| #20289767 | 2 |
| #20276318 | 2 |
| #12597 | 53 |