Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
452 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 98 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. #20290470 | C2 | semidirect |
| 4. #20289816 | C2 | semidirect |
| 9. #16811533 | C4 | semidirect |
| 10. #16811531 | C4 | semidirect |
| 18. #16810646 | C4 | semidirect |
| 20. #16810590 | C4 | semidirect |
| 21. C2×#13133127 | C4 | semidirect |
| 22. C2×#131×C53 | C4 | semidirect |
| 153. C2×#131 | #6157 | semidirect |
| 169. C53 | #12634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291006 | 2 |
| #20290986 | 2 |
| #20290470 | 2 |
| #20289816 | 2 |
| #20283431 | 2 |
| #12634 | 53 |