Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1424 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 545 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. #26012327 | C2 | semidirect |
| 2. #26012308 | C2 | semidirect |
| 3. #26012303 | C2 | semidirect |
| 4. #26012296 | C2 | semidirect |
| 5. #26012291 | C2 | semidirect |
| 6. C2×#19149701 | C2 | semidirect |
| 7. C2×#131×C173 | C2 | semidirect |
| 9. #19149726 | C22 | semidirect |
| 10. #19149725 | C22 | semidirect |
| 12. C2×#14583826 | C22 | semidirect |
| 14. #19149712 | C22 | semidirect |
| 15. #19149707 | C22 | semidirect |
| 16. #19149701 | C22 | semidirect |
| 17. #19149701 | C22 | semidirect |
| 18. #19149701 | C22 | semidirect |
| 19. #19149701 | C22 | semidirect |
| 20. C2×Dic692 | C22 | semidirect |
| 21. C2×#14583815 | C22 | semidirect |
| 22. C2×D1384 | C22 | semidirect |
| 24. #131×C173 | C22 | semidirect |
| 25. #131×C173 | C22 | semidirect |
| 26. C2×M16×C173 | C22 | semidirect |
| 27. C22×C8×C173 | C22 | semidirect |
| 89. C173 | #3584 | semidirect |
| 97. C2×#131 | D173 | semidirect |
| 114. #131 | C2×D173 | semidirect |
| 115. #131 | C2×D173 | semidirect |
| 116. C2×M16 | C2×D173 | semidirect |
| 117. C22×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012327 | 2 |
| #26012308 | 2 |
| #26012303 | 2 |
| #26012296 | 2 |
| #26012291 | 2 |
| C2×#19149701 | 2 |
| C2×#131×C173 | 2 |
| #3584 | 173 |