Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 1. D53⋊(C22⋊C16) | C2 | semidirect |
| 2. #20290592 | C2 | semidirect |
| 3. #20289702 | C2 | semidirect |
| 8. #16811518 | C22 | semidirect |
| 10. #16811497 | C22 | semidirect |
| 11. C22×D424 | C4 | semidirect |
| 16. #16810860 | C4 | semidirect |
| 19. C2×#107×C53 | C4 | semidirect |
| 174. C2×#107 | #6157 | semidirect |
| 180. C53 | #11886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C22⋊C16) | 2 |
| #20290592 | 2 |
| #20289702 | 2 |
| C2×#16810860 | 2 |
| #11886 | 53 |