Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 9. #16811019 | C4 | semidirect |
| 10. #16811002 | C4 | semidirect |
| 11. #16810975 | C4 | semidirect |
| 12. #16810973 | C4 | semidirect |
| 174. C53 | #9416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285456 | 2 |
| #20283820 | 2 |
| #20273353 | 2 |
| #20273265 | 2 |
| #20272588 | 2 |
| #20272579 | 2 |
| C53×#1515 | 2 |
| #9416 | 53 |