Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 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. #20285374 | C2 | semidirect |
| 3. #20276935 | C2 | semidirect |
| 4. #20276892 | C2 | semidirect |
| 5. #20276797 | C2 | semidirect |
| 7. #20276608 | C2 | semidirect |
| 8. C53×#2166 | C2 | semidirect |
| 13. #16811025 | C22 | semidirect |
| 14. #16811003 | C22 | semidirect |
| 22. #16810731 | C22 | semidirect |
| 26. #16810446 | C22 | semidirect |
| 27. #16810440 | C22 | semidirect |
| 30. C53×#364 | C22 | semidirect |
| 32. C53×#347 | C22 | semidirect |
| 164. #2166 | D53 | semidirect |
| 188. #364 | C2×D53 | semidirect |
| 192. #347 | C2×D53 | semidirect |
| 193. C53 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285374 | 2 |
| #20283619 | 2 |
| #20276935 | 2 |
| #20276892 | 2 |
| #20276797 | 2 |
| #20276668 | 2 |
| #20276608 | 2 |
| C53×#2166 | 2 |
| #33693 | 53 |