Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19149706 | C2 | semidirect |
| 2. #26012042 | C2 | semidirect |
| 3. #127×D173 | C2 | semidirect |
| 4. #26011877 | C2 | semidirect |
| 5. #26011868 | C2 | semidirect |
| 6. #26011867 | C2 | semidirect |
| 7. #26011865 | C2 | semidirect |
| 8. C4×#14583809 | C2 | semidirect |
| 9. #492×C173 | C2 | semidirect |
| 14. C2×#14583813 | C22 | semidirect |
| 15. C2×D1384 | C22 | semidirect |
| 16. C2×#14583811 | C22 | semidirect |
| 19. #19149676 | C22 | semidirect |
| 22. #19149668 | C22 | semidirect |
| 26. #19149589 | C22 | semidirect |
| 27. C4×#13063436 | C22 | semidirect |
| 28. C2×SD16×C173 | C22 | semidirect |
| 29. C4⋊Q8×C173 | C22 | semidirect |
| 31. C4×C8×C173 | C22 | semidirect |
| 49. #14583809 | D4 | semidirect |
| 78. #13063436 | C2×D4 | semidirect |
| 86. C8×C173 | C2×D4 | semidirect |
| 98. C4×C173 | AGL(1,ℤ/8) | semidirect |
| 108. C173 | #3151 | semidirect |
| 117. #492 | D173 | semidirect |
| 124. C2×SD16 | C2×D173 | semidirect |
| 128. C4⋊Q8 | C2×D173 | semidirect |
| 140. C4×C8 | C2×D173 | semidirect |
| 195. C8 | D4×D173 | semidirect |
| 209. C4 | #19149706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149706 | 2 |
| #26012042 | 2 |
| #127×D173 | 2 |
| #26011877 | 2 |
| #26011868 | 2 |
| #26011867 | 2 |
| #26011865 | 2 |
| C4×#14583809 | 2 |
| #492×C173 | 2 |
| #3151 | 173 |