Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
522 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 9. #16810378 | C4 | semidirect |
| 13. C53×#336 | C4 | semidirect |
| 19. C2×C4×Dic53 | C8 | semidirect |
| 160. #336 | Dic53 | semidirect |
| 161. C53 | #7017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274783 | 2 |
| C4×#13133124 | 2 |
| C53×#1817 | 2 |
| #7017 | 53 |