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 |
|---|---|---|
| 2. #26011815 | C2 | semidirect |
| 3. #26011815 | C2 | semidirect |
| 4. #26011809 | C2 | semidirect |
| 5. #26011804 | C2 | semidirect |
| 6. #26011531 | C2 | semidirect |
| 7. #26011527 | C2 | semidirect |
| 8. #26011495 | C2 | semidirect |
| 9. C2×#19149599 | C2 | semidirect |
| 10. #26011458 | C2 | semidirect |
| 11. #520×C173 | C2 | 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 |
| 38. #117×C173 | C22 | semidirect |
| 40. C2×C4⋊C4×C173 | C22 | semidirect |
| 134. C173 | #3096 | semidirect |
| 137. #520 | D173 | semidirect |
| 161. #117 | C2×D173 | semidirect |
| 163. C2×C4⋊C4 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012055 | 2 |
| #26011815 | 2 |
| #26011809 | 2 |
| #26011804 | 2 |
| #26011531 | 2 |
| #26011527 | 2 |
| #26011495 | 2 |
| C2×#19149599 | 2 |
| #26011458 | 2 |
| #520×C173 | 2 |
| #3096 | 173 |