Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
308 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 112 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. #16811548 | C4 | semidirect |
| 10. #16811547 | C4 | semidirect |
| 15. #16810398 | C4 | semidirect |
| 16. #16810398 | C4 | semidirect |
| 17. C4×#11719908 | C4 | semidirect |
| 18. C4×C16×C53 | C4 | semidirect |
| 110. C4×C16 | #6157 | semidirect |
| 112. C53 | #12668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291062 | 2 |
| #20290517 | 2 |
| #20289785 | 2 |
| #20289783 | 2 |
| C4×#13133156 | 2 |
| #12668 | 53 |