Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26012042 | C2 | semidirect |
| 2. #124×D173 | C2 | semidirect |
| 3. #26011881 | C2 | semidirect |
| 4. #26011880 | C2 | semidirect |
| 5. #26011853 | C2 | semidirect |
| 6. #26011709 | C2 | semidirect |
| 7. #26011705 | C2 | semidirect |
| 8. #26011631 | C2 | semidirect |
| 9. #26011626 | C2 | semidirect |
| 10. #26011546 | C2 | semidirect |
| 11. #489×C173 | C2 | semidirect |
| 15. C2×#14583815 | C22 | semidirect |
| 16. C2×#14583813 | C22 | semidirect |
| 19. #19149676 | C22 | semidirect |
| 29. #19149641 | C22 | semidirect |
| 33. #19149608 | C22 | semidirect |
| 34. #19149602 | C22 | semidirect |
| 37. #19149590 | C22 | semidirect |
| 38. C4⋊Q8×C173 | C22 | semidirect |
| 40. #103×C173 | C22 | semidirect |
| 42. #97×C173 | C22 | semidirect |
| 150. C173 | #3213 | semidirect |
| 157. #489 | D173 | semidirect |
| 170. C4⋊Q8 | C2×D173 | semidirect |
| 188. #103 | C2×D173 | semidirect |
| 193. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012042 | 2 |
| #124×D173 | 2 |
| #26011881 | 2 |
| #26011880 | 2 |
| #26011853 | 2 |
| #26011709 | 2 |
| #26011705 | 2 |
| #26011631 | 2 |
| #26011626 | 2 |
| #26011546 | 2 |
| #489×C173 | 2 |
| #3213 | 173 |