Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
396 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 225. C53 | #9528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291621 | 2 |
| #20290251 | 2 |
| #20290045 | 2 |
| #20289979 | 2 |
| #20289620 | 2 |
| #20289573 | 2 |
| #20284842 | 2 |
| #9528 | 53 |