Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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. #16811545 | C4 | semidirect |
| 14. C8×#88322 | C4 | semidirect |
| 15. C82×C53 | C4 | semidirect |
| 22. #13133287 | C8 | semidirect |
| 24. #13133285 | C8 | semidirect |
| 116. C82 | #6157 | semidirect |
| 117. C53 | #7180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#364 | 2 |
| #20290517 | 2 |
| #20272997 | 2 |
| #7180 | 53 |