Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 3. #20290473 | C2 | semidirect |
| 4. #20290472 | C2 | semidirect |
| 5. #20289805 | C2 | semidirect |
| 6. #20289802 | C2 | semidirect |
| 9. C22×#11719940 | C4 | semidirect |
| 14. #16811629 | C4 | semidirect |
| 18. #16811593 | C4 | semidirect |
| 21. #16811587 | C4 | semidirect |
| 22. #16811526 | C4 | semidirect |
| 23. #16811523 | C4 | semidirect |
| 29. #16810414 | C4 | semidirect |
| 30. #16810412 | C4 | semidirect |
| 31. #16810410 | C4 | semidirect |
| 32. C53×AΣL(1,𝔽16) | C4 | semidirect |
| 245. AΣL(1,𝔽16) | #6157 | semidirect |
| 248. C53 | #12624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291434 | 2 |
| #20290967 | 2 |
| #20290473 | 2 |
| #20290472 | 2 |
| #20289805 | 2 |
| #20289802 | 2 |
| #20276353 | 2 |
| #12624 | 53 |