Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20273266 | C2 | semidirect |
| 5. #20272586 | C2 | semidirect |
| 6. #20272581 | C2 | semidirect |
| 7. C53×#1537 | C2 | semidirect |
| 9. #16811026 | C4 | semidirect |
| 10. #16810997 | C4 | semidirect |
| 11. #16810973 | C4 | semidirect |
| 12. #16810971 | C4 | semidirect |
| 157. #1537 | D53 | semidirect |
| 186. C53 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285434 | 2 |
| #20283785 | 2 |
| #20273266 | 2 |
| #20273263 | 2 |
| #20272586 | 2 |
| #20272581 | 2 |
| C53×#1537 | 2 |
| #9415 | 53 |