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. C2×#19149726 | C2 | semidirect |
| 2. #26012306 | C2 | semidirect |
| 3. #26012302 | C2 | semidirect |
| 4. #26012289 | C2 | semidirect |
| 5. C2×#19149709 | C2 | semidirect |
| 6. #26012258 | C2 | semidirect |
| 7. #585×C173 | C2 | semidirect |
| 9. #19149726 | C22 | semidirect |
| 10. C2×#14583826 | C22 | semidirect |
| 12. C22×Dic346 | C22 | semidirect |
| 14. #19149710 | C22 | semidirect |
| 15. #19149709 | C22 | semidirect |
| 16. #19149709 | C22 | semidirect |
| 17. #19149705 | C22 | semidirect |
| 18. #19149704 | C22 | semidirect |
| 19. #19149699 | C22 | semidirect |
| 20. C2×#14583816 | C22 | semidirect |
| 21. C2×#14583814 | C22 | semidirect |
| 22. #19149686 | C22 | semidirect |
| 23. C2×#14583810 | C22 | semidirect |
| 25. 2−1+4×C173 | C22 | semidirect |
| 27. H(5,𝔽2)×C173 | C22 | semidirect |
| 112. C173 | #3586 | semidirect |
| 114. #585 | D173 | semidirect |
| 124. 2−1+4 | C2×D173 | semidirect |
| 126. H(5,𝔽2) | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149726 | 2 |
| #26012306 | 2 |
| #26012302 | 2 |
| #26012289 | 2 |
| C2×#19149709 | 2 |
| #26012258 | 2 |
| #585×C173 | 2 |
| #3586 | 173 |