Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
458 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. #20283805 | C2 | semidirect |
| 3. #20274548 | C2 | semidirect |
| 6. #20272613 | C2 | semidirect |
| 7. C53×#1285 | C2 | semidirect |
| 11. #16810919 | C4 | semidirect |
| 12. #16810919 | C4 | semidirect |
| 13. #16810824 | C4 | semidirect |
| 14. #16810824 | C4 | semidirect |
| 204. #1285 | D53 | semidirect |
| 236. C53 | #9164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284838 | 2 |
| #20283805 | 2 |
| #20274548 | 2 |
| #20273327 | 2 |
| #20273209 | 2 |
| #20272613 | 2 |
| C53×#1285 | 2 |
| #9164 | 53 |