Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×D16×D53 | C2 | semidirect |
| 2. C2×D1696 | C2 | semidirect |
| 3. C2×#16810458 | C2 | semidirect |
| 4. D32×D53 | C2 | direct (N × H) |
| 5. C2×C32×D53 | C2 | semidirect |
| 6. C2×C53×D32 | C2 | semidirect |
| 8. C2×D848 | C22 | semidirect |
| 11. D16×D53 | C22 | semidirect |
| 13. D1696 | C22 | semidirect |
| 14. #16810458 | C22 | semidirect |
| 15. C2×#13133123 | C22 | semidirect |
| 16. C32×D53 | C22 | semidirect |
| 17. C2×D16×C53 | C22 | semidirect |
| 18. C53×D32 | C22 | semidirect |
| 19. C2×C32×C53 | C22 | semidirect |
| 27. D848 | C23 | semidirect |
| 32. #13133123 | C23 | semidirect |
| 35. D16×C53 | C23 | semidirect |
| 37. C32×C53 | C23 | semidirect |
| 81. C2×D53 | D32 | direct (N × H) |
| 90. C2×D32 | D53 | direct (N × H) |
| 93. C2×C53 | C2×D32 | semidirect |
| 96. D53 | C2×D32 | direct (N × H) |
| 102. C2×D16 | C2×D53 | semidirect |
| 106. D32 | C2×D53 | direct (N × H) |
| 109. C2×C32 | C2×D53 | semidirect |
| 110. C53 | C22×D32 | semidirect |
| 122. D16 | C22×D53 | semidirect |
| 128. C32 | C22×D53 | semidirect |
| 179. C2 | D32×D53 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D53 | 2 |
| C2×D1696 | 2 |
| C2×#16810458 | 2 |
| D32×D53 | 2 |
| C2×C32×D53 | 2 |
| C2×C53×D32 | 2 |
| C22×D32 | 53 |