Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 68 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. #16811519 | C4 | semidirect |
| 13. #16810405 | C4 | semidirect |
| 15. C53×#349 | C4 | semidirect |
| 149. #349 | #6157 | semidirect |
| 152. C53 | #7191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#349 | 2 |
| #20290377 | 2 |
| #349×D53 | 2 |
| #7191 | 53 |