Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 134 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. #16811485 | C4 | semidirect |
| 13. #16811484 | C4 | semidirect |
| 17. #16810345 | C4 | semidirect |
| 18. #16810345 | C4 | semidirect |
| 19. #16810344 | C4 | semidirect |
| 20. C53×#322 | C4 | semidirect |
| 91. C8×C53 | #97 | semidirect |
| 95. #88322 | #97 | semidirect |
| 134. #322 | #6157 | semidirect |
| 135. C53 | #8287 | semidirect |
| 210. C8 | #13133271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133286 | 2 |
| #20290509 | 2 |
| D53⋊#334 | 2 |
| #20289550 | 2 |
| #322×D53 | 2 |
| #8287 | 53 |