Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26012027 | C2 | semidirect |
| 2. C2×#19149666 | C2 | semidirect |
| 3. #26011872 | C2 | semidirect |
| 4. #26011844 | C2 | semidirect |
| 5. #26011711 | C2 | semidirect |
| 6. #26011705 | C2 | semidirect |
| 7. #26011646 | C2 | semidirect |
| 8. #26011632 | C2 | semidirect |
| 10. #26011541 | C2 | semidirect |
| 11. #450×C173 | C2 | semidirect |
| 13. C2×#14583816 | C22 | semidirect |
| 14. C2×#14583815 | C22 | semidirect |
| 17. #19149670 | C22 | semidirect |
| 18. #19149668 | C22 | semidirect |
| 25. Q8×Dic173 | C22 | semidirect |
| 26. #19149641 | C22 | semidirect |
| 32. #19149608 | C22 | semidirect |
| 33. #19149604 | C22 | semidirect |
| 34. #19149602 | C22 | semidirect |
| 37. C8×Dic173 | C22 | semidirect |
| 143. C173 | #3211 | semidirect |
| 152. #450 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012027 | 2 |
| C2×#19149666 | 2 |
| #26011872 | 2 |
| #26011844 | 2 |
| #26011711 | 2 |
| #26011705 | 2 |
| #26011646 | 2 |
| #26011632 | 2 |
| #26011625 | 2 |
| #26011541 | 2 |
| #450×C173 | 2 |
| #3211 | 173 |