Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
954 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 2. #20289595 | C2 | semidirect |
| 5. #16811566 | C4 | semidirect |
| 7. #16811565 | C4 | semidirect |
| 12. C22×#11719917 | C4 | semidirect |
| 14. #16810586 | C4 | semidirect |
| 17. C22×M16×C53 | C4 | semidirect |
| 196. C22×M16 | #6157 | semidirect |
| 208. C53 | #8049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291159 | 2 |
| #20289595 | 2 |
| C2×#16810586 | 2 |
| #8049 | 53 |