Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 213. C53 | #9336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291627 | 2 |
| #20290241 | 2 |
| #20290197 | 2 |
| #20289988 | 2 |
| #20289622 | 2 |
| #20289573 | 2 |
| #20285920 | 2 |
| #9336 | 53 |