Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 12. #16811514 | C4 | semidirect |
| 13. #16811513 | C4 | semidirect |
| 14. #16811512 | C4 | semidirect |
| 15. C4×#11719910 | C4 | semidirect |
| 18. #16810399 | C4 | semidirect |
| 19. C16×Dic53 | C4 | semidirect |
| 20. C53×#346 | C4 | semidirect |
| 111. #346 | #6157 | semidirect |
| 114. C53 | #12541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811514 | 2 |
| C2×#16811513 | 2 |
| C4×#13133292 | 2 |
| #20290371 | 2 |
| #20276308 | 2 |
| #12541 | 53 |