Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
854 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. #20275893 | C2 | semidirect |
| 2. #20275891 | C2 | semidirect |
| 3. #20275879 | C2 | semidirect |
| 5. C53×#2029 | C2 | semidirect |
| 7. #16811249 | C22 | semidirect |
| 11. #16810390 | C22 | semidirect |
| 12. #16810389 | C22 | semidirect |
| 13. C53×#543 | C22 | semidirect |
| 15. C53×#342 | C22 | semidirect |
| 16. C24×D53 | Q8 | semidirect |
| 19. C22×C22⋊D53 | Q8 | semidirect |
| 21. C23×Dic53 | Q8 | semidirect |
| 120. #2029 | D53 | semidirect |
| 131. #543 | C2×D53 | semidirect |
| 138. #342 | C2×D53 | semidirect |
| 139. C53 | #32873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275893 | 2 |
| #20275891 | 2 |
| #20275879 | 2 |
| #20274629 | 2 |
| C53×#2029 | 2 |
| #32873 | 53 |