Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
418 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
|---|---|---|
| 37. #97×C53 | C8 | semidirect |
| 83. C8×C53 | C4⋊C8 | semidirect |
| 121. C53 | #8808 | semidirect |
| 139. #97 | #88324 | semidirect |
| 188. C8 | C4⋊#88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290647 | 2 |
| #20290630 | 2 |
| C2×#16811486 | 2 |
| C2×#16811484 | 2 |
| #97×Dic53 | 2 |
| #8808 | 53 |