Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 11. #16811487 | C4 | semidirect |
| 12. #16811484 | C4 | semidirect |
| 17. #16810376 | C4 | semidirect |
| 18. #16810373 | C4 | semidirect |
| 19. C53×#335 | C4 | semidirect |
| 122. #335 | #6157 | semidirect |
| 127. C53 | #8269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133271 | 2 |
| #20290263 | 2 |
| #20289931 | 2 |
| #20289542 | 2 |
| #20273462 | 2 |
| #8269 | 53 |