Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1424 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 750 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. #26012570 | C2 | semidirect |
| 2. #26012569 | C2 | semidirect |
| 3. D173⋊#131 | C2 | semidirect |
| 4. C2×#19149766 | C2 | semidirect |
| 6. #19149767 | C22 | semidirect |
| 7. #19149767 | C22 | semidirect |
| 8. #19149766 | C22 | semidirect |
| 9. #19149766 | C22 | semidirect |
| 10. #19149766 | C22 | semidirect |
| 11. C2×#14583836 | C22 | semidirect |
| 12. D173⋊M16 | C22 | semidirect |
| 13. C2×#14583835 | C22 | semidirect |
| 14. C2×D173⋊C8 | C22 | semidirect |
| 15. C22×#13063443 | C22 | semidirect |
| 66. C173 | #3573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012570 | 2 |
| #26012569 | 2 |
| D173⋊#131 | 2 |
| C2×#19149766 | 2 |
| #26012326 | 2 |
| #3573 | 173 |