Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 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. #20273224 | C2 | semidirect |
| 3. #20273223 | C2 | semidirect |
| 4. #20273185 | C2 | semidirect |
| 5. #20272578 | C2 | semidirect |
| 6. #20272543 | C2 | semidirect |
| 7. C53×#2981 | C2 | semidirect |
| 9. #16810999 | C4 | semidirect |
| 10. #16810995 | C4 | semidirect |
| 11. #16810975 | C4 | semidirect |
| 12. #16810971 | C4 | semidirect |
| 174. #2981 | D53 | semidirect |
| 207. C53 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285644 | 2 |
| #20273224 | 2 |
| #20273223 | 2 |
| #20273185 | 2 |
| #20272578 | 2 |
| #20272543 | 2 |
| C53×#2981 | 2 |
| #9281 | 53 |