Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
376 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 188. C53 | #8246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290220 | 2 |
| #20290172 | 2 |
| #20289924 | 2 |
| C8×#11719940 | 2 |
| #20289599 | 2 |
| #20283648 | 2 |
| #8246 | 53 |