Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. C2×#16811513 | C2 | semidirect |
| 4. #20289755 | C2 | semidirect |
| 7. C2×#13133292 | C4 | semidirect |
| 10. C22×#11719910 | C4 | semidirect |
| 18. C22⋊#11719908 | C4 | semidirect |
| 19. #16810402 | C4 | semidirect |
| 20. C53×C22⋊C16 | C4 | semidirect |
| 78. #11719910 | C22⋊C4 | semidirect |
| 112. C22×C53 | #347 | semidirect |
| 150. C22⋊C16 | #6157 | semidirect |
| 153. C53 | #12616 | semidirect |
| 251. C22 | #16811513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133292 | 2 |
| C2×#16811513 | 2 |
| #20290451 | 2 |
| #20289755 | 2 |
| #20276324 | 2 |
| #12616 | 53 |