Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
766 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 766 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. #26012326 | C2 | semidirect |
| 2. #26011999 | C2 | semidirect |
| 3. #26011680 | C2 | semidirect |
| 4. #26011679 | C2 | semidirect |
| 5. #26011678 | C2 | semidirect |
| 6. #26011463 | C2 | semidirect |
| 7. #458×C173 | C2 | semidirect |
| 14. C22×C4×D173 | C22 | semidirect |
| 15. #19149662 | C22 | semidirect |
| 18. #19149649 | C22 | semidirect |
| 19. #19149647 | C22 | semidirect |
| 22. #19149635 | C22 | semidirect |
| 23. #19149594 | C22 | semidirect |
| 24. #19149593 | C22 | semidirect |
| 26. #123×C173 | C22 | semidirect |
| 27. #99×C173 | C22 | semidirect |
| 38. C2×Dic346 | D4 | semidirect |
| 44. C2×C22⋊D173 | D4 | semidirect |
| 49. C22×Dic173 | D4 | semidirect |
| 54. C2×C4×D173 | D4 | semidirect |
| 126. C173 | #3025 | semidirect |
| 131. #458 | D173 | semidirect |
| 144. #123 | C2×D173 | semidirect |
| 154. #99 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012326 | 2 |
| #26011999 | 2 |
| #26011680 | 2 |
| #26011679 | 2 |
| #26011678 | 2 |
| #26011463 | 2 |
| #458×C173 | 2 |
| #3025 | 173 |