Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
448 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. #20276409 | C2 | semidirect |
| 4. #20276368 | C2 | semidirect |
| 6. #20274765 | C2 | semidirect |
| 7. C53×#1757 | C2 | semidirect |
| 8. C22×#11719913 | C4 | semidirect |
| 16. #16810661 | C4 | semidirect |
| 17. #16810633 | C4 | semidirect |
| 18. #16810629 | C4 | semidirect |
| 211. #1757 | D53 | semidirect |
| 241. C53 | #13232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284354 | 2 |
| #20276409 | 2 |
| #20276406 | 2 |
| #20276368 | 2 |
| #20276364 | 2 |
| #20274765 | 2 |
| C53×#1757 | 2 |
| #13232 | 53 |