Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. C4×#13133150 | C2 | semidirect |
| 3. #20273476 | C2 | semidirect |
| 6. #20272572 | C2 | semidirect |
| 7. C53×#1285 | C2 | semidirect |
| 9. #16810750 | C4 | semidirect |
| 10. #16810747 | C4 | semidirect |
| 11. #16810700 | C4 | semidirect |
| 13. #16810688 | C4 | semidirect |
| 179. #1285 | D53 | semidirect |
| 209. C53 | #8697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283684 | 2 |
| C4×#13133150 | 2 |
| #20273476 | 2 |
| #20273241 | 2 |
| #20273238 | 2 |
| #20272572 | 2 |
| C53×#1285 | 2 |
| #8697 | 53 |