Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
302 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 108 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. #16810398 | C4 | semidirect |
| 14. C4×#11719908 | C4 | semidirect |
| 15. C4×C16×C53 | C4 | semidirect |
| 117. C4×C16 | #6157 | semidirect |
| 118. C53 | #12886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290654 | 2 |
| #20290650 | 2 |
| #20289780 | 2 |
| C4×#13133156 | 2 |
| #12886 | 53 |