Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 98 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×#16811548 | C2 | semidirect |
| 4. #20289780 | C2 | semidirect |
| 17. C22⋊#11719908 | C4 | semidirect |
| 18. #16810402 | C4 | semidirect |
| 19. C53×C22⋊C16 | C4 | semidirect |
| 123. C22×C53 | #365 | semidirect |
| 166. C22⋊C16 | #6157 | semidirect |
| 168. C53 | #12928 | semidirect |
| 280. C22 | #16811548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133287 | 2 |
| C2×#16811548 | 2 |
| #20290591 | 2 |
| #20289780 | 2 |
| #20276324 | 2 |
| #12928 | 53 |