Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
698 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 1. #20290572 | C2 | semidirect |
| 3. #20289891 | C2 | semidirect |
| 4. #20289588 | C2 | semidirect |
| 14. C2×D4×Dic53 | C4 | semidirect |
| 17. #16810521 | C4 | semidirect |
| 21. C4⋊C4×Dic53 | C4 | semidirect |
| 23. C53×#390 | C4 | semidirect |
| 245. #390 | #6157 | semidirect |
| 257. C53 | #8573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290572 | 2 |
| C2×#16811474 | 2 |
| #20289891 | 2 |
| #20289588 | 2 |
| #20277231 | 2 |
| #8573 | 53 |