Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19149705 | C2 | semidirect |
| 2. #26012162 | C2 | semidirect |
| 3. #26011867 | C2 | semidirect |
| 4. #26011742 | C2 | semidirect |
| 5. #26011688 | C2 | semidirect |
| 6. #26011686 | C2 | semidirect |
| 7. #26011634 | C2 | semidirect |
| 8. #26011625 | C2 | semidirect |
| 9. C4×#14583814 | C2 | semidirect |
| 10. #26011569 | C2 | semidirect |
| 11. D42×C173 | C2 | semidirect |
| 12. C2×#14583826 | C22 | semidirect |
| 15. C2×#14583814 | C22 | semidirect |
| 17. C2×#14583811 | C22 | semidirect |
| 18. C2×#14583811 | C22 | semidirect |
| 19. C2×#14583810 | C22 | semidirect |
| 20. #19149676 | C22 | semidirect |
| 22. #19149653 | C22 | semidirect |
| 24. C4×Dic346 | C22 | semidirect |
| 26. #19149610 | C22 | semidirect |
| 27. C4⋊#13063436 | C22 | semidirect |
| 28. #19149602 | C22 | semidirect |
| 30. #19149600 | C22 | semidirect |
| 31. #19149599 | C22 | semidirect |
| 32. C22⋊#13063436 | C22 | semidirect |
| 33. C4×#13063436 | C22 | semidirect |
| 52. #14583814 | D4 | semidirect |
| 85. Dic346 | C2×D4 | semidirect |
| 97. #13063436 | C2×D4 | semidirect |
| 138. C4×C173 | AGL(1,ℤ/8) | semidirect |
| 150. C173 | #3274 | semidirect |
| 154. D42 | D173 | semidirect |
| 291. C4 | #19149705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149705 | 2 |
| #26012162 | 2 |
| #26011867 | 2 |
| #26011742 | 2 |
| #26011688 | 2 |
| #26011686 | 2 |
| #26011634 | 2 |
| #26011625 | 2 |
| C4×#14583814 | 2 |
| #26011569 | 2 |
| D42×C173 | 2 |
| #3274 | 173 |