Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012096 | C2 | semidirect |
| 2. #26011881 | C2 | semidirect |
| 3. #26011867 | C2 | semidirect |
| 4. #26011855 | C2 | semidirect |
| 5. #26011845 | C2 | semidirect |
| 6. #26011703 | C2 | semidirect |
| 7. #26011683 | C2 | semidirect |
| 8. #26011636 | C2 | semidirect |
| 9. #26011625 | C2 | semidirect |
| 10. #26011552 | C2 | semidirect |
| 11. #535×C173 | C2 | semidirect |
| 12. C2×#14583813 | C22 | semidirect |
| 15. C2×#14583811 | C22 | semidirect |
| 16. #19149676 | C22 | semidirect |
| 17. #19149671 | C22 | semidirect |
| 21. C4×D692 | C22 | semidirect |
| 22. C4⋊#13063436 | C22 | semidirect |
| 23. #19149603 | C22 | semidirect |
| 26. #19149600 | C22 | semidirect |
| 28. #19149590 | C22 | semidirect |
| 29. C4×#13063436 | C22 | semidirect |
| 128. C173 | #3220 | semidirect |
| 131. #535 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012096 | 2 |
| #26011881 | 2 |
| #26011867 | 2 |
| #26011855 | 2 |
| #26011845 | 2 |
| #26011703 | 2 |
| #26011683 | 2 |
| #26011636 | 2 |
| #26011625 | 2 |
| #26011552 | 2 |
| #535×C173 | 2 |
| #3220 | 173 |