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. #26012022 | C2 | semidirect |
| 2. C2×D4×Dic173 | C2 | semidirect |
| 3. #26011822 | C2 | semidirect |
| 4. #26011802 | C2 | semidirect |
| 5. #26011793 | C2 | semidirect |
| 6. #26011704 | C2 | semidirect |
| 7. #26011642 | C2 | semidirect |
| 8. #26011603 | C2 | semidirect |
| 9. #26011588 | C2 | semidirect |
| 10. #26011545 | C2 | semidirect |
| 15. #19149670 | C22 | semidirect |
| 16. #19149666 | C22 | semidirect |
| 19. #19149644 | C22 | semidirect |
| 25. D4×Dic173 | C22 | semidirect |
| 30. #19149612 | C22 | semidirect |
| 31. #19149611 | C22 | semidirect |
| 32. #19149608 | C22 | semidirect |
| 33. #19149604 | C22 | semidirect |
| 35. #19149600 | C22 | semidirect |
| 37. #19149589 | C22 | semidirect |
| 140. C173 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012022 | 2 |
| C2×D4×Dic173 | 2 |
| #26011822 | 2 |
| #26011802 | 2 |
| #26011793 | 2 |
| #26011704 | 2 |
| #26011642 | 2 |
| #26011603 | 2 |
| #26011588 | 2 |
| #26011545 | 2 |
| #447×C173 | 2 |
| #3114 | 173 |