Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
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×D89 | C2 | semidirect |
| 2. C2×D2848 | C2 | semidirect |
| 3. C2×#19151433 | C2 | semidirect |
| 4. D32×D89 | C2 | direct (N × H) |
| 5. C2×C32×D89 | C2 | semidirect |
| 6. C2×D32×C89 | C2 | semidirect |
| 8. C2×D1424 | C22 | semidirect |
| 11. D16×D89 | C22 | semidirect |
| 13. D2848 | C22 | semidirect |
| 14. #19151433 | C22 | semidirect |
| 15. C2×#15667918 | C22 | semidirect |
| 16. C32×D89 | C22 | semidirect |
| 17. C2×D16×C89 | C22 | semidirect |
| 18. D32×C89 | C22 | semidirect |
| 19. C2×C32×C89 | C22 | semidirect |
| 27. D1424 | C23 | semidirect |
| 32. #15667918 | C23 | semidirect |
| 35. D16×C89 | C23 | semidirect |
| 37. C32×C89 | C23 | semidirect |
| 80. C2×D89 | D32 | direct (N × H) |
| 87. C2×C89 | C2×D32 | semidirect |
| 90. D89 | C2×D32 | direct (N × H) |
| 95. C2×D32 | D89 | direct (N × H) |
| 97. C89 | C22×D32 | semidirect |
| 103. C2×D16 | C2×D89 | semidirect |
| 107. D32 | C2×D89 | direct (N × H) |
| 110. C2×C32 | C2×D89 | semidirect |
| 122. D16 | C22×D89 | semidirect |
| 128. C32 | C22×D89 | semidirect |
| 179. C2 | D32×D89 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D89 | 2 |
| C2×D2848 | 2 |
| C2×#19151433 | 2 |
| D32×D89 | 2 |
| C2×C32×D89 | 2 |
| C2×D32×C89 | 2 |
| C22×D32 | 89 |