Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26012292 | C2 | semidirect |
| 2. #26011927 | C2 | semidirect |
| 3. #26011925 | C2 | semidirect |
| 4. #26011923 | C2 | semidirect |
| 5. #26011920 | C2 | semidirect |
| 6. D16×D173 | C2 | semidirect |
| 7. #26011907 | C2 | semidirect |
| 8. C2×D16×C173 | C2 | semidirect |
| 12. #19149701 | C22 | semidirect |
| 13. #19149698 | C22 | semidirect |
| 14. D8×D173 | C22 | semidirect |
| 16. Dic1384 | C22 | semidirect |
| 17. #19149624 | C22 | semidirect |
| 18. #19149623 | C22 | semidirect |
| 19. D2768 | C22 | semidirect |
| 20. #19149620 | C22 | semidirect |
| 21. #19149619 | C22 | semidirect |
| 22. #19149618 | C22 | semidirect |
| 23. C16×D173 | C22 | semidirect |
| 24. C2×D8×C173 | C22 | semidirect |
| 25. D16×C173 | C22 | semidirect |
| 26. D16×C173 | C22 | semidirect |
| 27. C2×C16×C173 | C22 | semidirect |
| 84. C173 | #3415 | semidirect |
| 92. C2×D16 | D173 | semidirect |
| 100. C2×D8 | C2×D173 | semidirect |
| 107. D16 | C2×D173 | semidirect |
| 108. D16 | C2×D173 | semidirect |
| 112. C2×C16 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012292 | 2 |
| #26011927 | 2 |
| #26011925 | 2 |
| #26011923 | 2 |
| #26011920 | 2 |
| D16×D173 | 2 |
| #26011907 | 2 |
| C2×D16×C173 | 2 |
| #3415 | 173 |