Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
334 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 13. #16810651 | C4 | semidirect |
| 14. #16810649 | C4 | semidirect |
| 18. M16×Dic53 | C4 | semidirect |
| 19. C2×#13133127 | C4 | semidirect |
| 193. C53 | #12865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283362 | 2 |
| #20274820 | 2 |
| #20274816 | 2 |
| #20272844 | 2 |
| #20272837 | 2 |
| #20272835 | 2 |
| C53×#1395 | 2 |
| #12865 | 53 |