Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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×D4×Dic173 | C2 | semidirect |
| 3. #26011819 | C2 | semidirect |
| 4. #26011805 | C2 | semidirect |
| 5. #26011789 | C2 | semidirect |
| 6. #26011708 | C2 | semidirect |
| 8. #26011600 | C2 | semidirect |
| 9. #26011592 | C2 | semidirect |
| 10. #26011545 | C2 | semidirect |
| 11. #450×C173 | C2 | semidirect |
| 15. #19149670 | C22 | semidirect |
| 16. #19149668 | C22 | semidirect |
| 19. Q8×Dic173 | C22 | semidirect |
| 24. #19149641 | C22 | semidirect |
| 30. #19149613 | C22 | semidirect |
| 31. #19149610 | C22 | semidirect |
| 32. #19149608 | C22 | semidirect |
| 33. #19149603 | C22 | semidirect |
| 34. #19149601 | C22 | semidirect |
| 37. #19149589 | C22 | semidirect |
| 140. C173 | #3114 | semidirect |
| 148. #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×D4×Dic173 | 2 |
| #26011819 | 2 |
| #26011805 | 2 |
| #26011789 | 2 |
| #26011708 | 2 |
| #26011625 | 2 |
| #26011600 | 2 |
| #26011592 | 2 |
| #26011545 | 2 |
| #450×C173 | 2 |
| #3114 | 173 |