Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 7. #16811028 | C4 | semidirect |
| 8. #16811003 | C4 | semidirect |
| 9. #16810974 | C4 | semidirect |
| 154. C53 | #9720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285301 | 2 |
| #20275659 | 2 |
| C4×#13133149 | 2 |
| #20273215 | 2 |
| C53×#1451 | 2 |
| #9720 | 53 |