Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19149701 | C2 | semidirect |
| 2. #26011932 | C2 | semidirect |
| 3. #26011931 | C2 | semidirect |
| 4. #26011927 | C2 | semidirect |
| 5. #26011926 | C2 | semidirect |
| 6. #26011921 | C2 | semidirect |
| 7. C2×#19149619 | C2 | semidirect |
| 8. C2×#135×C173 | C2 | semidirect |
| 13. #19149701 | C22 | semidirect |
| 14. C2×Dic692 | C22 | semidirect |
| 16. C2×D1384 | C22 | semidirect |
| 17. #19149625 | C22 | semidirect |
| 18. #19149623 | C22 | semidirect |
| 19. #19149622 | C22 | semidirect |
| 20. #19149620 | C22 | semidirect |
| 21. #19149619 | C22 | semidirect |
| 22. #19149619 | C22 | semidirect |
| 23. C2×#14583801 | C22 | semidirect |
| 28. #135×C173 | C22 | semidirect |
| 29. C2×Q16×C173 | C22 | semidirect |
| 31. C2×D8×C173 | C22 | semidirect |
| 120. C173 | #3414 | semidirect |
| 123. C2×#135 | D173 | semidirect |
| 139. #135 | C2×D173 | semidirect |
| 141. C2×Q16 | C2×D173 | semidirect |
| 145. C2×D8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| #26011932 | 2 |
| #26011931 | 2 |
| #26011927 | 2 |
| #26011926 | 2 |
| #26011921 | 2 |
| C2×#19149619 | 2 |
| C2×#135×C173 | 2 |
| #3414 | 173 |