Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
382 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 17. #16810374 | C4 | semidirect |
| 18. #16810373 | C4 | semidirect |
| 19. C53×#334 | C4 | semidirect |
| 100. C8×C53 | #107 | semidirect |
| 103. #88322 | #107 | semidirect |
| 144. #334 | #6157 | semidirect |
| 145. C53 | #9611 | semidirect |
| 229. C8 | #13133286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290826 | 2 |
| #20290650 | 2 |
| C8×C4⋊#6157 | 2 |
| #20289594 | 2 |
| #334×D53 | 2 |
| #9611 | 53 |