Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
326 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 13. #16811516 | C4 | semidirect |
| 14. #16811515 | C4 | semidirect |
| 17. #16810401 | C4 | semidirect |
| 18. #16810400 | C4 | semidirect |
| 19. C53×#347 | C4 | semidirect |
| 128. #347 | #6157 | semidirect |
| 129. C53 | #12595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290932 | 2 |
| #97×#6157 | 2 |
| #20289761 | 2 |
| #20289758 | 2 |
| #347×D53 | 2 |
| #12595 | 53 |