Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 32. #13133153 | C8 | semidirect |
| 127. C53 | #9607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290268 | 2 |
| C2×#16811484 | 2 |
| #20289918 | 2 |
| #20289561 | 2 |
| #108×Dic53 | 2 |
| #9607 | 53 |