Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
296 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 10. #16811546 | C4 | semidirect |
| 11. #16811545 | C4 | semidirect |
| 18. #16810399 | C4 | semidirect |
| 19. C16×Dic53 | C4 | semidirect |
| 20. C16×Dic53 | C4 | semidirect |
| 21. C53×#346 | C4 | semidirect |
| 129. #346 | #6157 | semidirect |
| 133. C53 | #12667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#364 | 2 |
| #20290934 | 2 |
| #20290517 | 2 |
| #20289764 | 2 |
| #20276308 | 2 |
| #12667 | 53 |