Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #20285460 | C2 | semidirect |
| 3. #20276935 | C2 | semidirect |
| 4. #20276887 | C2 | semidirect |
| 5. #20276797 | C2 | semidirect |
| 7. #20276608 | C2 | semidirect |
| 8. C53×#2165 | C2 | semidirect |
| 13. #16811021 | C22 | semidirect |
| 14. #16811003 | C22 | semidirect |
| 23. #16810731 | C22 | semidirect |
| 26. #16810446 | C22 | semidirect |
| 27. #16810440 | C22 | semidirect |
| 30. C53×#364 | C22 | semidirect |
| 32. C53×#347 | C22 | semidirect |
| 165. #2165 | D53 | semidirect |
| 189. #364 | C2×D53 | semidirect |
| 193. #347 | C2×D53 | semidirect |
| 194. C53 | #33689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285460 | 2 |
| #20283626 | 2 |
| #20276935 | 2 |
| #20276887 | 2 |
| #20276797 | 2 |
| #20276668 | 2 |
| #20276608 | 2 |
| C53×#2165 | 2 |
| #33689 | 53 |