Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #26011972 | C2 | semidirect |
| 3. #26011818 | C2 | semidirect |
| 4. #26011817 | C2 | semidirect |
| 5. #26011811 | C2 | semidirect |
| 6. #26011806 | C2 | semidirect |
| 7. #26011527 | C2 | semidirect |
| 8. #26011497 | C2 | semidirect |
| 9. C2×#19149599 | C2 | semidirect |
| 10. #26011459 | C2 | semidirect |
| 11. #428×C173 | C2 | semidirect |
| 24. #19149637 | C22 | semidirect |
| 25. C4⋊C4×D173 | C22 | semidirect |
| 26. #19149612 | C22 | semidirect |
| 27. #19149612 | C22 | semidirect |
| 28. #19149610 | C22 | semidirect |
| 29. #19149610 | C22 | semidirect |
| 34. #19149591 | C22 | semidirect |
| 35. #19149591 | C22 | semidirect |
| 39. #107×C173 | C22 | semidirect |
| 40. #106×C173 | C22 | semidirect |
| 134. C173 | #3096 | semidirect |
| 142. #428 | D173 | semidirect |
| 166. #107 | C2×D173 | semidirect |
| 169. #106 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012060 | 2 |
| #26011972 | 2 |
| #26011818 | 2 |
| #26011817 | 2 |
| #26011811 | 2 |
| #26011806 | 2 |
| #26011527 | 2 |
| #26011497 | 2 |
| C2×#19149599 | 2 |
| #26011459 | 2 |
| #428×C173 | 2 |
| #3096 | 173 |