Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 174. C53 | #9420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291629 | 2 |
| #20290249 | 2 |
| #20290245 | 2 |
| #20290207 | 2 |
| #20289582 | 2 |
| #20285258 | 2 |
| #9420 | 53 |