Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
262 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 8. #16811509 | C4 | semidirect |
| 13. #16810374 | C4 | semidirect |
| 14. C53×#334 | C4 | semidirect |
| 20. #13133285 | C8 | semidirect |
| 105. #334 | #6157 | semidirect |
| 106. C53 | #7174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290922 | 2 |
| C4×#13133285 | 2 |
| #20273460 | 2 |
| #7174 | 53 |