Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 12. #16810345 | C4 | semidirect |
| 13. #16810345 | C4 | semidirect |
| 14. #16810344 | C4 | semidirect |
| 15. C8×#88322 | C4 | semidirect |
| 120. C53 | #8803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20273018 | 2 |
| #20272588 | 2 |
| #20272587 | 2 |
| #20272586 | 2 |
| #20272579 | 2 |
| C53×#1288 | 2 |
| #8803 | 53 |