Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #20274803 | C2 | semidirect |
| 4. #20274793 | C2 | semidirect |
| 5. #20272621 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 10. #16810951 | C4 | semidirect |
| 12. #16810934 | C4 | semidirect |
| 247. C53 | #9521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284635 | 2 |
| #20283763 | 2 |
| #20274803 | 2 |
| #20274793 | 2 |
| #20272621 | 2 |
| #20272591 | 2 |
| C53×#1513 | 2 |
| #9521 | 53 |