Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26012122 | C2 | semidirect |
| 3. #26011793 | C2 | semidirect |
| 4. #26011789 | C2 | semidirect |
| 5. #26011779 | C2 | semidirect |
| 6. #26011769 | C2 | semidirect |
| 7. #26011531 | C2 | semidirect |
| 8. #26011529 | C2 | semidirect |
| 9. #26011517 | C2 | semidirect |
| 14. #19149678 | C22 | semidirect |
| 16. #19149670 | C22 | semidirect |
| 26. #19149613 | C22 | semidirect |
| 27. #19149613 | C22 | semidirect |
| 28. #19149612 | C22 | semidirect |
| 29. #19149611 | C22 | semidirect |
| 30. #19149611 | C22 | semidirect |
| 31. #19149610 | C22 | semidirect |
| 32. #19149608 | C22 | semidirect |
| 33. #19149608 | C22 | semidirect |
| 66. C2×D4×C173 | Q8 | semidirect |
| 124. C173 | #3081 | semidirect |
| 170. C2×D4 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012122 | 2 |
| #26011966 | 2 |
| #26011793 | 2 |
| #26011789 | 2 |
| #26011779 | 2 |
| #26011769 | 2 |
| #26011531 | 2 |
| #26011529 | 2 |
| #26011517 | 2 |
| #26011496 | 2 |
| C2×#102×C173 | 2 |
| #3081 | 173 |