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. #26011971 | C2 | semidirect |
| 3. #26011818 | C2 | semidirect |
| 4. #26011817 | C2 | semidirect |
| 5. #26011811 | C2 | semidirect |
| 6. #26011806 | C2 | semidirect |
| 7. #26011534 | C2 | semidirect |
| 8. #26011495 | C2 | semidirect |
| 9. C2×#19149601 | C2 | semidirect |
| 10. #26011457 | C2 | semidirect |
| 11. #427×C173 | C2 | semidirect |
| 23. #19149637 | C22 | semidirect |
| 25. C4⋊C4×D173 | C22 | semidirect |
| 26. #19149612 | C22 | semidirect |
| 27. #19149610 | C22 | semidirect |
| 32. #19149591 | C22 | semidirect |
| 33. #19149591 | C22 | semidirect |
| 37. #107×C173 | C22 | semidirect |
| 38. #107×C173 | C22 | semidirect |
| 39. #106×C173 | C22 | semidirect |
| 40. #106×C173 | C22 | semidirect |
| 134. C173 | #3096 | semidirect |
| 143. #427 | D173 | semidirect |
| 165. #107 | C2×D173 | semidirect |
| 166. #107 | C2×D173 | semidirect |
| 168. #106 | 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 |
| #26011971 | 2 |
| #26011818 | 2 |
| #26011817 | 2 |
| #26011811 | 2 |
| #26011806 | 2 |
| #26011534 | 2 |
| #26011495 | 2 |
| C2×#19149601 | 2 |
| #26011457 | 2 |
| #427×C173 | 2 |
| #3096 | 173 |