Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 104 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. #20290932 | C2 | semidirect |
| 4. #20290521 | C2 | semidirect |
| 5. #20289788 | C2 | semidirect |
| 6. #20289779 | C2 | semidirect |
| 13. #16811541 | C4 | semidirect |
| 14. #16811535 | C4 | semidirect |
| 20. #16810736 | C4 | semidirect |
| 21. #16810735 | C4 | semidirect |
| 22. #16810734 | C4 | semidirect |
| 28. C53×#442 | C4 | semidirect |
| 32. #13133292 | C2×C4 | semidirect |
| 36. D53⋊C16 | C2×C4 | semidirect |
| 38. #13133287 | C2×C4 | semidirect |
| 39. #13133286 | C2×C4 | semidirect |
| 205. #442 | #6157 | semidirect |
| 217. C53 | #12647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#361 | 2 |
| #20291024 | 2 |
| #20290932 | 2 |
| #20290521 | 2 |
| #20289788 | 2 |
| #20289779 | 2 |
| #442×D53 | 2 |
| #12647 | 53 |