Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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. C2×#19149699 | C2 | semidirect |
| 3. C22×#14583811 | C2 | semidirect |
| 4. #26012058 | C2 | semidirect |
| 5. #26012055 | C2 | semidirect |
| 6. #26011879 | C2 | semidirect |
| 7. #26011877 | C2 | semidirect |
| 8. #26011872 | C2 | semidirect |
| 9. #26011866 | C2 | semidirect |
| 10. #26011449 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C173 | C2 | semidirect |
| 16. C2×#14583816 | C22 | semidirect |
| 17. C2×#14583815 | C22 | semidirect |
| 18. C2×#14583814 | C22 | semidirect |
| 19. C2×#14583813 | C22 | semidirect |
| 20. C2×D1384 | C22 | semidirect |
| 24. C2×#14583811 | C22 | semidirect |
| 26. #19149675 | C22 | semidirect |
| 27. #19149675 | C22 | semidirect |
| 28. #19149668 | C22 | semidirect |
| 29. #19149666 | C22 | semidirect |
| 35. #19149589 | C22 | semidirect |
| 36. C8×Dic173 | C22 | semidirect |
| 40. C2×SD16×C173 | C22 | semidirect |
| 41. C2×D8×C173 | C22 | semidirect |
| 64. C2×#13063436 | D4 | semidirect |
| 86. M16×C173 | D4 | semidirect |
| 153. C173 | #3155 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D173 | semidirect |
| 177. C2×SD16 | C2×D173 | semidirect |
| 183. C2×D8 | C2×D173 | semidirect |
| 232. 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 |
| C2×#19149699 | 2 |
| C22×#14583811 | 2 |
| #26012058 | 2 |
| #26012055 | 2 |
| #26011879 | 2 |
| #26011877 | 2 |
| #26011872 | 2 |
| #26011866 | 2 |
| #26011449 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| #3155 | 173 |