Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
428 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 17. #16810365 | C4 | semidirect |
| 18. #16810364 | C4 | semidirect |
| 19. C53×#330 | C4 | semidirect |
| 137. #330 | #6157 | semidirect |
| 138. C53 | #8913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291261 | 2 |
| #20290898 | 2 |
| #20290653 | 2 |
| #20289592 | 2 |
| #330×D53 | 2 |
| #8913 | 53 |