Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 414 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. C2×#19149637 | C2 | semidirect |
| 3. #26011835 | C2 | semidirect |
| 4. #26011834 | C2 | semidirect |
| 5. #26011818 | C2 | semidirect |
| 6. #26011817 | C2 | semidirect |
| 7. #26011534 | C2 | semidirect |
| 8. #26011493 | C2 | semidirect |
| 9. #26011490 | C2 | semidirect |
| 10. #26011454 | C2 | semidirect |
| 11. #428×C173 | C2 | semidirect |
| 30. #19149612 | C22 | semidirect |
| 31. #19149610 | C22 | semidirect |
| 32. #19149604 | C22 | semidirect |
| 33. #19149602 | C22 | semidirect |
| 34. #19149601 | C22 | semidirect |
| 35. #19149599 | C22 | semidirect |
| 41. #107×C173 | C22 | semidirect |
| 42. #106×C173 | C22 | semidirect |
| 152. C173 | #3093 | semidirect |
| 161. #428 | D173 | semidirect |
| 187. #107 | C2×D173 | semidirect |
| 189. #106 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012003 | 2 |
| C2×#19149637 | 2 |
| #26011835 | 2 |
| #26011834 | 2 |
| #26011818 | 2 |
| #26011817 | 2 |
| #26011534 | 2 |
| #26011493 | 2 |
| #26011490 | 2 |
| #26011454 | 2 |
| #428×C173 | 2 |
| #3093 | 173 |