Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 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. #26012062 | C2 | semidirect |
| 2. #26011832 | C2 | semidirect |
| 3. #26011812 | C2 | semidirect |
| 4. #26011735 | C2 | semidirect |
| 5. #26011718 | C2 | semidirect |
| 6. #26011642 | C2 | semidirect |
| 7. #26011629 | C2 | semidirect |
| 8. #26011458 | C2 | semidirect |
| 10. C22×Dic346 | C22 | semidirect |
| 13. C2×#14583810 | C22 | semidirect |
| 14. C22×#13063436 | C22 | semidirect |
| 20. #19149658 | C22 | semidirect |
| 21. #19149638 | C22 | semidirect |
| 22. #19149612 | C22 | semidirect |
| 23. #19149610 | C22 | semidirect |
| 24. #19149602 | C22 | semidirect |
| 25. #19149602 | C22 | semidirect |
| 29. C22⋊#13063436 | C22 | semidirect |
| 137. C173 | #3200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012062 | 2 |
| #26011832 | 2 |
| #26011812 | 2 |
| #26011735 | 2 |
| #26011718 | 2 |
| #26011642 | 2 |
| #26011629 | 2 |
| #26011458 | 2 |
| #535×C173 | 2 |
| #3200 | 173 |