Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19149653 | C2 | semidirect |
| 2. #26011824 | C2 | semidirect |
| 3. #26011815 | C2 | semidirect |
| 4. #26011807 | C2 | semidirect |
| 5. #26011725 | C2 | semidirect |
| 6. #26011722 | C2 | semidirect |
| 7. #26011641 | C2 | semidirect |
| 8. #26011636 | C2 | semidirect |
| 9. #26011624 | C2 | semidirect |
| 10. C2×C22⋊#13063436 | C2 | semidirect |
| 11. #525×C173 | C2 | semidirect |
| 14. C2×#14583813 | C22 | semidirect |
| 15. C2×#14583811 | C22 | semidirect |
| 16. C22×#13063436 | C22 | semidirect |
| 23. #19149612 | C22 | semidirect |
| 24. #19149610 | C22 | semidirect |
| 25. #19149603 | C22 | semidirect |
| 26. #19149600 | C22 | semidirect |
| 27. #19149599 | C22 | semidirect |
| 28. #19149599 | C22 | semidirect |
| 31. C22⋊#13063436 | C22 | semidirect |
| 32. C2×#41×C173 | C22 | semidirect |
| 36. C22⋊Q8×C173 | C22 | semidirect |
| 38. #121×C173 | C22 | semidirect |
| 42. #117×C173 | C22 | semidirect |
| 158. C173 | #3188 | semidirect |
| 160. #525 | D173 | semidirect |
| 171. C2×#41 | C2×D173 | semidirect |
| 180. C22⋊Q8 | C2×D173 | semidirect |
| 186. #121 | C2×D173 | semidirect |
| 190. #117 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149653 | 2 |
| #26011824 | 2 |
| #26011815 | 2 |
| #26011807 | 2 |
| #26011725 | 2 |
| #26011722 | 2 |
| #26011641 | 2 |
| #26011636 | 2 |
| #26011624 | 2 |
| C2×C22⋊#13063436 | 2 |
| #525×C173 | 2 |
| #3188 | 173 |