Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
292 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 292 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 |
|---|---|---|
| 14. #16811552 | C4 | semidirect |
| 15. #16811551 | C4 | semidirect |
| 16. #16811548 | C4 | semidirect |
| 17. #16811547 | C4 | semidirect |
| 23. #16810401 | C4 | semidirect |
| 24. #16810400 | C4 | semidirect |
| 25. #16810400 | C4 | semidirect |
| 26. C53×#347 | C4 | semidirect |
| 155. #347 | #6157 | semidirect |
| 158. C53 | #12678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291071 | 2 |
| #20291063 | 2 |
| #20290535 | 2 |
| #20290521 | 2 |
| #20289796 | 2 |
| #20289793 | 2 |
| #347×D53 | 2 |
| #12678 | 53 |