Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 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. C2×#19149726 | C2 | semidirect |
| 3. #26012308 | C2 | semidirect |
| 4. #26012303 | C2 | semidirect |
| 5. #26012291 | C2 | semidirect |
| 6. C2×#19149712 | C2 | semidirect |
| 7. #568×C173 | C2 | semidirect |
| 10. #19149726 | C22 | semidirect |
| 11. #19149726 | C22 | semidirect |
| 12. #19149725 | C22 | semidirect |
| 15. C2×#14583826 | C22 | semidirect |
| 18. C22×Dic346 | C22 | semidirect |
| 20. #19149712 | C22 | semidirect |
| 21. #19149712 | C22 | semidirect |
| 22. #19149712 | C22 | semidirect |
| 23. #19149707 | C22 | semidirect |
| 24. #19149707 | C22 | semidirect |
| 25. #19149701 | C22 | semidirect |
| 26. C2×Dic692 | C22 | semidirect |
| 27. C2×#14583815 | C22 | semidirect |
| 29. #131×C173 | C22 | semidirect |
| 30. C2×M16×C173 | C22 | semidirect |
| 112. C173 | #3586 | semidirect |
| 120. #568 | D173 | semidirect |
| 142. #131 | C2×D173 | semidirect |
| 143. C2×M16 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012327 | 2 |
| C2×#19149726 | 2 |
| #26012308 | 2 |
| #26012303 | 2 |
| #26012291 | 2 |
| C2×#19149712 | 2 |
| #568×C173 | 2 |
| #3586 | 173 |