Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #20272595 | C2 | semidirect |
| 4. #20272583 | C2 | semidirect |
| 11. #16810489 | C4 | semidirect |
| 12. #16810483 | C4 | semidirect |
| 15. C4×C4⋊Dic53 | C4 | semidirect |
| 16. C2×#13133124 | C4 | semidirect |
| 212. C53 | #8760 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277625 | 2 |
| #20274703 | 2 |
| #20272595 | 2 |
| #20272583 | 2 |
| C53×#1459 | 2 |
| #8760 | 53 |