Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 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×#19149712 | C2 | semidirect |
| 3. C2×#19149666 | C2 | semidirect |
| 4. #26011959 | C2 | semidirect |
| 5. #26011712 | C2 | semidirect |
| 6. #26011705 | C2 | semidirect |
| 7. #26011514 | C2 | semidirect |
| 8. #26011499 | C2 | semidirect |
| 9. #418×C173 | C2 | semidirect |
| 14. C2×Dic692 | C22 | semidirect |
| 15. C2×#14583815 | C22 | semidirect |
| 22. #19149644 | C22 | semidirect |
| 23. #19149641 | C22 | semidirect |
| 29. #19149608 | C22 | semidirect |
| 30. #19149602 | C22 | semidirect |
| 125. C173 | #3040 | semidirect |
| 135. #418 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149712 | 2 |
| C2×#19149705 | 2 |
| C2×#19149666 | 2 |
| #26011959 | 2 |
| #26011712 | 2 |
| #26011705 | 2 |
| #26011514 | 2 |
| #26011499 | 2 |
| #418×C173 | 2 |
| #3040 | 173 |