Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26012119 | C2 | semidirect |
| 2. #26011855 | C2 | semidirect |
| 3. #26011850 | C2 | semidirect |
| 4. #26011845 | C2 | semidirect |
| 5. #26011837 | C2 | semidirect |
| 6. #26011496 | C2 | semidirect |
| 7. #26011492 | C2 | semidirect |
| 8. #26011487 | C2 | semidirect |
| 9. C2×#19149600 | C2 | semidirect |
| 10. #26011447 | C2 | semidirect |
| 14. #19149679 | C22 | semidirect |
| 16. #19149671 | C22 | semidirect |
| 21. #19149603 | C22 | semidirect |
| 22. #19149603 | C22 | semidirect |
| 23. #19149603 | C22 | semidirect |
| 28. #19149600 | C22 | semidirect |
| 29. #19149600 | C22 | semidirect |
| 30. #19149600 | C22 | semidirect |
| 31. #19149590 | C22 | semidirect |
| 32. C4×#13063436 | C22 | semidirect |
| 135. C173 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012119 | 2 |
| #26011855 | 2 |
| #26011850 | 2 |
| #26011845 | 2 |
| #26011837 | 2 |
| #26011496 | 2 |
| #26011492 | 2 |
| #26011487 | 2 |
| C2×#19149600 | 2 |
| #26011447 | 2 |
| #535×C173 | 2 |
| #3136 | 173 |