Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2070 conjugacy classes of subgroups; only the 416 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 416 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 |
|---|---|---|
| 2. #20289903 | C2 | semidirect |
| 9. C2×#13133124 | C4 | semidirect |
| 10. #95×D53 | C4 | semidirect |
| 12. C2×#95×C53 | C4 | semidirect |
| 39. C22×C4×C53 | C4⋊C4 | semidirect |
| 42. C22×Dic53 | C4⋊C4 | semidirect |
| 48. C2×C4×D53 | C4⋊C4 | semidirect |
| 121. C2×#95 | #6157 | semidirect |
| 122. C53 | #14353 | semidirect |
| 159. C22×C4 | C4⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811565 | 2 |
| #20289903 | 2 |
| C2×#95×D53 | 2 |
| #14353 | 53 |