Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
788 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 10. #16810646 | C4 | semidirect |
| 12. M16×Dic53 | C4 | semidirect |
| 14. #16810474 | C4 | semidirect |
| 17. #16810468 | C4 | semidirect |
| 154. C53 | #8048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283344 | 2 |
| C4×#13133173 | 2 |
| #20272601 | 2 |
| #20272600 | 2 |
| C53×#1297 | 2 |
| #8048 | 53 |