Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×D848 | C2 | semidirect |
| 2. C2×#16810458 | C2 | direct (N × H) |
| 3. C22×#13133123 | C2 | semidirect |
| 4. C22×D16×C53 | C2 | semidirect |
| 7. C2×D848 | C22 | semidirect |
| 8. #16810458 | C22 | direct (N × H) |
| 9. C2×#13133123 | C22 | semidirect |
| 12. C2×D16×C53 | C22 | semidirect |
| 18. D848 | C23 | semidirect |
| 19. #13133123 | C23 | semidirect |
| 25. D16×C53 | C23 | semidirect |
| 59. C22×C53 | D32 | semidirect |
| 66. C22×D16 | D53 | semidirect |
| 70. C2×C53 | C2×D32 | semidirect |
| 78. C2×D16 | C2×D53 | semidirect |
| 82. C53 | C22×D32 | semidirect |
| 93. D16 | C22×D53 | semidirect |
| 129. C22 | #16810458 | direct (N × H) |
| 135. C2 | C2×#16810458 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D848 | 2 |
| C2×#16810458 | 2 |
| C22×#13133123 | 2 |
| C22×D16×C53 | 2 |
| C22×D32 | 53 |