Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 109 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. #16810375 | C4 | semidirect |
| 19. #16810373 | C4 | semidirect |
| 146. C53 | #9632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274852 | 2 |
| #20274584 | 2 |
| #20273490 | 2 |
| #20273487 | 2 |
| #20273461 | 2 |
| #20272618 | 2 |
| C53×#1303 | 2 |
| #9632 | 53 |