Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 104 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. #16811028 | C4 | semidirect |
| 14. #16811024 | C4 | semidirect |
| 19. C53×#500 | C4 | semidirect |
| 22. #13133292 | Q8 | semidirect |
| 131. #500 | #6157 | semidirect |
| 143. C53 | #13288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290922 | 2 |
| #20290652 | 2 |
| #20289786 | 2 |
| #20285226 | 2 |
| #13288 | 53 |