Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
358 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 13. #16811546 | C4 | semidirect |
| 14. #16811545 | C4 | semidirect |
| 19. #16810444 | C4 | semidirect |
| 20. #16810443 | C4 | semidirect |
| 21. C53×#364 | C4 | semidirect |
| 135. #364 | #6157 | semidirect |
| 138. C53 | #12656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#364 | 2 |
| M32×#6157 | 2 |
| #20290371 | 2 |
| #20289758 | 2 |
| #364×D53 | 2 |
| #12656 | 53 |