Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1082 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1082 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. #20286093 | C2 | semidirect |
| 2. #20285141 | C2 | semidirect |
| 3. #20273860 | C2 | semidirect |
| 4. #20273831 | C2 | semidirect |
| 5. #20273798 | C2 | semidirect |
| 6. #20273769 | C2 | semidirect |
| 7. #20273450 | C2 | semidirect |
| 8. #20273166 | C2 | semidirect |
| 9. C53×#3549 | C2 | semidirect |
| 11. #16811173 | C22 | semidirect |
| 13. #16811002 | C22 | semidirect |
| 15. #16810997 | C22 | semidirect |
| 17. #16810913 | C22 | semidirect |
| 20. #16810818 | C22 | semidirect |
| 22. #16810647 | C22 | semidirect |
| 23. C2×C4×#88322 | C22 | semidirect |
| 24. #16810372 | C22 | semidirect |
| 26. D4⋊#88322 | C22 | semidirect |
| 27. D4⋊#88322 | C22 | semidirect |
| 200. #3549 | D53 | semidirect |
| 242. C53 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286093 | 2 |
| #20285141 | 2 |
| #20273860 | 2 |
| #20273831 | 2 |
| #20273798 | 2 |
| #20273769 | 2 |
| #20273450 | 2 |
| #20273166 | 2 |
| C53×#3549 | 2 |
| #18686 | 53 |