Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149707 | C2 | semidirect |
| 2. #26012069 | C2 | semidirect |
| 3. #26012055 | C2 | semidirect |
| 4. #26011744 | C2 | semidirect |
| 5. #26011737 | C2 | semidirect |
| 6. #26011727 | C2 | semidirect |
| 7. #26011720 | C2 | semidirect |
| 8. #26011533 | C2 | semidirect |
| 9. #26011488 | C2 | semidirect |
| 10. C2×#19149601 | C2 | semidirect |
| 11. C2×#131×C173 | C2 | semidirect |
| 19. #19149658 | C22 | semidirect |
| 23. #19149653 | C22 | semidirect |
| 29. #19149613 | C22 | semidirect |
| 30. #19149611 | C22 | semidirect |
| 31. #19149604 | C22 | semidirect |
| 32. #19149604 | C22 | semidirect |
| 35. #19149601 | C22 | semidirect |
| 36. #19149601 | C22 | semidirect |
| 40. C2×M16×C173 | C22 | semidirect |
| 42. C22×C8×C173 | C22 | semidirect |
| 79. M16×C173 | D4 | semidirect |
| 151. C173 | #3062 | semidirect |
| 154. C2×#131 | D173 | semidirect |
| 172. C2×M16 | C2×D173 | semidirect |
| 174. C22×C8 | C2×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×#19149707 | 2 |
| #26012069 | 2 |
| #26012055 | 2 |
| #26011744 | 2 |
| #26011737 | 2 |
| #26011727 | 2 |
| #26011720 | 2 |
| #26011533 | 2 |
| #26011488 | 2 |
| C2×#19149601 | 2 |
| C2×#131×C173 | 2 |
| #3062 | 173 |