Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
996 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 179 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. #20286102 | C2 | semidirect |
| 2. #20285037 | C2 | semidirect |
| 3. #20273943 | C2 | semidirect |
| 4. #20273894 | C2 | semidirect |
| 5. #20273450 | C2 | semidirect |
| 6. #20273166 | C2 | semidirect |
| 8. #16811180 | C22 | semidirect |
| 10. #16810973 | C22 | semidirect |
| 13. #16810903 | C22 | semidirect |
| 15. #16810828 | C22 | semidirect |
| 17. #16810647 | C22 | semidirect |
| 19. C2×C4×#88322 | C22 | semidirect |
| 20. #16810372 | C22 | semidirect |
| 22. D4⋊#88322 | C22 | semidirect |
| 211. C53 | #18691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286102 | 2 |
| #20285037 | 2 |
| #20273943 | 2 |
| #20273894 | 2 |
| #20273450 | 2 |
| #20273166 | 2 |
| C53×#3549 | 2 |
| #18691 | 53 |