Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19149658 | C2 | semidirect |
| 2. #26011832 | C2 | semidirect |
| 3. #26011819 | C2 | semidirect |
| 4. #26011802 | C2 | semidirect |
| 5. #26011730 | C2 | semidirect |
| 6. #26011718 | C2 | semidirect |
| 7. #26011653 | C2 | semidirect |
| 8. #26011646 | C2 | semidirect |
| 9. #26011629 | C2 | semidirect |
| 10. C2×C22⋊#13063436 | C2 | semidirect |
| 13. C2×#14583816 | C22 | semidirect |
| 14. C2×#14583814 | C22 | semidirect |
| 23. #19149612 | C22 | semidirect |
| 24. #19149610 | C22 | semidirect |
| 25. #19149603 | C22 | semidirect |
| 26. #19149602 | C22 | semidirect |
| 27. #19149602 | C22 | semidirect |
| 28. #19149600 | C22 | semidirect |
| 149. C173 | #3190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149658 | 2 |
| #26011832 | 2 |
| #26011819 | 2 |
| #26011802 | 2 |
| #26011730 | 2 |
| #26011718 | 2 |
| #26011653 | 2 |
| #26011646 | 2 |
| #26011629 | 2 |
| C2×C22⋊#13063436 | 2 |
| #525×C173 | 2 |
| #3190 | 173 |