Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19149704 | C2 | semidirect |
| 2. C22×#14583811 | C2 | semidirect |
| 3. #26011965 | C2 | semidirect |
| 4. #26011703 | C2 | semidirect |
| 5. #26011683 | C2 | semidirect |
| 6. #26011518 | C2 | semidirect |
| 7. #26011496 | C2 | semidirect |
| 8. #26011487 | C2 | semidirect |
| 9. #535×C173 | C2 | semidirect |
| 12. C2×#14583813 | C22 | semidirect |
| 15. C2×#14583811 | C22 | semidirect |
| 18. C4×D692 | C22 | semidirect |
| 22. C4⋊#13063436 | C22 | semidirect |
| 23. #19149603 | C22 | semidirect |
| 24. #19149600 | C22 | semidirect |
| 25. #19149600 | C22 | semidirect |
| 28. #127×C173 | C22 | semidirect |
| 29. #124×C173 | C22 | semidirect |
| 36. C2×D692 | D4 | semidirect |
| 121. C173 | #3041 | semidirect |
| 125. #535 | D173 | semidirect |
| 142. #127 | C2×D173 | semidirect |
| 143. #124 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149704 | 2 |
| C22×#14583811 | 2 |
| #26011965 | 2 |
| #26011703 | 2 |
| #26011683 | 2 |
| #26011518 | 2 |
| #26011496 | 2 |
| #26011487 | 2 |
| #535×C173 | 2 |
| #3041 | 173 |