Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1252 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1252 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. #20285168 | C2 | semidirect |
| 2. #20274004 | C2 | semidirect |
| 3. #20273307 | C2 | semidirect |
| 4. C53×#3549 | C2 | semidirect |
| 6. C2×#13133214 | C22 | semidirect |
| 7. #16811013 | C22 | semidirect |
| 10. C4×#11719917 | C22 | semidirect |
| 11. #16810363 | C22 | semidirect |
| 12. C53×H(3,𝔽4) | C22 | semidirect |
| 93. #3549 | D53 | semidirect |
| 102. H(3,𝔽4) | C2×D53 | semidirect |
| 113. C53 | #19073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285168 | 2 |
| #20274004 | 2 |
| #20273307 | 2 |
| C53×#3549 | 2 |
| #19073 | 53 |