Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012055 | C2 | semidirect |
| 2. #26011815 | C2 | semidirect |
| 3. #26011812 | C2 | semidirect |
| 4. #26011742 | C2 | semidirect |
| 5. #26011725 | C2 | semidirect |
| 6. #26011625 | C2 | semidirect |
| 7. #26011624 | C2 | semidirect |
| 8. #26011458 | C2 | semidirect |
| 9. #535×C173 | C2 | semidirect |
| 10. C22×D692 | C22 | semidirect |
| 13. C2×#14583810 | C22 | semidirect |
| 14. C22×#13063436 | C22 | semidirect |
| 18. #19149653 | C22 | semidirect |
| 21. #19149638 | C22 | semidirect |
| 22. #19149612 | C22 | semidirect |
| 23. #19149610 | C22 | semidirect |
| 24. #19149600 | C22 | semidirect |
| 25. #19149600 | C22 | semidirect |
| 26. #19149599 | C22 | semidirect |
| 27. #19149599 | C22 | semidirect |
| 28. C22⋊#13063436 | C22 | semidirect |
| 29. C22⋊#13063436 | C22 | semidirect |
| 31. C22×D4×C173 | C22 | semidirect |
| 35. #121×C173 | C22 | semidirect |
| 38. #117×C173 | C22 | semidirect |
| 144. C173 | #3199 | semidirect |
| 147. #535 | D173 | semidirect |
| 157. C22×D4 | C2×D173 | semidirect |
| 169. #121 | C2×D173 | semidirect |
| 175. #117 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012055 | 2 |
| #26011815 | 2 |
| #26011812 | 2 |
| #26011742 | 2 |
| #26011725 | 2 |
| #26011625 | 2 |
| #26011624 | 2 |
| #26011458 | 2 |
| #535×C173 | 2 |
| #3199 | 173 |