Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
510 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 8. C22×#11719925 | C4 | semidirect |
| 15. C2×#13133150 | C4 | semidirect |
| 17. C2×#13133141 | C4 | semidirect |
| 18. C2×#13133140 | C4 | semidirect |
| 250. C53 | #9784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810862 | 2 |
| #20275701 | 2 |
| #20275699 | 2 |
| #20274738 | 2 |
| #20274494 | 2 |
| #20273288 | 2 |
| C53×#1520 | 2 |
| #9784 | 53 |