Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #26012454 | C2 | semidirect |
| 4. C2×C8×#10621924 | C2 | semidirect |
| 5. #26012366 | C2 | semidirect |
| 6. #26012363 | C2 | semidirect |
| 12. #19149744 | C4 | semidirect |
| 13. #19149743 | C4 | semidirect |
| 14. #19149742 | C4 | semidirect |
| 15. #19149741 | C4 | semidirect |
| 22. #19149687 | C4 | semidirect |
| 23. #19149686 | C4 | semidirect |
| 25. #19149685 | C4 | semidirect |
| 30. #131×C173 | C4 | semidirect |
| 127. C173 | #1764 | semidirect |
| 142. #131 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊#104 | 2 |
| #26012481 | 2 |
| #26012454 | 2 |
| C2×C8×#10621924 | 2 |
| #26012366 | 2 |
| #26012363 | 2 |
| #131×D173 | 2 |
| #1764 | 173 |