Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26012137 | C2 | semidirect |
| 3. #26011875 | C2 | semidirect |
| 4. #26011737 | C2 | semidirect |
| 5. #26011707 | C2 | semidirect |
| 6. #26011655 | C2 | semidirect |
| 7. #26011627 | C2 | semidirect |
| 8. C4×D1384 | C2 | semidirect |
| 9. #436×C173 | C2 | semidirect |
| 11. C22×D692 | C22 | semidirect |
| 13. C2×Dic692 | C22 | semidirect |
| 14. C2×#14583815 | C22 | semidirect |
| 15. C2×#14583815 | C22 | semidirect |
| 19. #19149667 | C22 | semidirect |
| 21. #19149658 | C22 | semidirect |
| 25. C4×D692 | C22 | semidirect |
| 27. #19149613 | C22 | semidirect |
| 28. #19149604 | C22 | semidirect |
| 29. #19149601 | C22 | semidirect |
| 30. #19149601 | C22 | semidirect |
| 31. C2×M16×C173 | C22 | semidirect |
| 33. C4⋊C8×C173 | C22 | semidirect |
| 34. C22⋊C8×C173 | C22 | semidirect |
| 35. C4×C8×C173 | C22 | semidirect |
| 54. D1384 | D4 | semidirect |
| 124. C173 | #3273 | semidirect |
| 134. #436 | D173 | semidirect |
| 144. C2×M16 | C2×D173 | semidirect |
| 155. C4⋊C8 | C2×D173 | semidirect |
| 159. C22⋊C8 | C2×D173 | semidirect |
| 160. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149707 | 2 |
| #26012137 | 2 |
| #26011875 | 2 |
| #26011737 | 2 |
| #26011707 | 2 |
| #26011655 | 2 |
| #26011627 | 2 |
| C4×D1384 | 2 |
| #436×C173 | 2 |
| #3273 | 173 |