Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#19149687 | C2 | semidirect |
| 2. #26012069 | C2 | semidirect |
| 3. #26012058 | C2 | semidirect |
| 4. #26011741 | C2 | semidirect |
| 5. #26011734 | C2 | semidirect |
| 6. #26011724 | C2 | semidirect |
| 7. #26011717 | C2 | semidirect |
| 8. #26011533 | C2 | semidirect |
| 9. #26011487 | C2 | semidirect |
| 10. C2×#19149600 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C173 | C2 | semidirect |
| 14. C2×#14583809 | C22 | semidirect |
| 16. C2×C8×D173 | C22 | semidirect |
| 20. #19149655 | C22 | semidirect |
| 25. #19149650 | C22 | semidirect |
| 29. #19149613 | C22 | semidirect |
| 30. #19149611 | C22 | semidirect |
| 31. #19149603 | C22 | semidirect |
| 32. #19149603 | C22 | semidirect |
| 35. #19149600 | C22 | semidirect |
| 36. #19149600 | C22 | semidirect |
| 83. M16×C173 | D4 | semidirect |
| 151. C173 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D173 | semidirect |
| 220. M16 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149687 | 2 |
| #26012069 | 2 |
| #26012058 | 2 |
| #26011741 | 2 |
| #26011734 | 2 |
| #26011724 | 2 |
| #26011717 | 2 |
| #26011533 | 2 |
| #26011487 | 2 |
| C2×#19149600 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| #3062 | 173 |