Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26011974 | C2 | semidirect |
| 2. #26011812 | C2 | semidirect |
| 3. #26011812 | C2 | semidirect |
| 4. #26011807 | C2 | semidirect |
| 5. #26011802 | C2 | semidirect |
| 6. #26011534 | C2 | semidirect |
| 7. #26011527 | C2 | semidirect |
| 8. #26011496 | C2 | semidirect |
| 9. C2×#19149600 | C2 | semidirect |
| 10. #26011458 | C2 | semidirect |
| 18. #19149638 | C22 | semidirect |
| 20. C2×C4⋊Dic173 | C22 | semidirect |
| 21. #19149612 | C22 | semidirect |
| 22. #19149612 | C22 | semidirect |
| 23. #19149612 | C22 | semidirect |
| 24. #19149610 | C22 | semidirect |
| 25. #19149610 | C22 | semidirect |
| 26. #19149610 | C22 | semidirect |
| 31. C22⋊#13063436 | C22 | semidirect |
| 32. C22⋊#13063436 | C22 | semidirect |
| 134. C173 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011974 | 2 |
| #26011812 | 2 |
| #26011807 | 2 |
| #26011802 | 2 |
| #26011534 | 2 |
| #26011527 | 2 |
| #26011496 | 2 |
| C2×#19149600 | 2 |
| #26011458 | 2 |
| #535×C173 | 2 |
| #3096 | 173 |