Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
214 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 3. #20289825 | C2 | semidirect |
| 4. #20289824 | C2 | semidirect |
| 9. #16811555 | C4 | semidirect |
| 10. D53⋊C32 | C4 | semidirect |
| 14. #16810456 | C4 | semidirect |
| 15. #16810456 | C4 | semidirect |
| 18. C2×#13133123 | C4 | semidirect |
| 19. C2×C32×C53 | C4 | semidirect |
| 100. C2×C32 | #6157 | semidirect |
| 103. C53 | #13551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊M64 | 2 |
| #20290923 | 2 |
| #20289825 | 2 |
| #20289824 | 2 |
| C2×#16810456 | 2 |
| #13551 | 53 |