Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19149658 | C2 | semidirect |
| 2. #26011821 | C2 | semidirect |
| 3. #26011807 | C2 | semidirect |
| 4. #26011718 | C2 | semidirect |
| 5. #26011642 | C2 | semidirect |
| 6. #26011629 | C2 | semidirect |
| 7. C2×C22⋊#13063436 | C2 | semidirect |
| 9. C22×Dic346 | C22 | semidirect |
| 10. C2×#14583814 | C22 | semidirect |
| 11. C22×#13063436 | C22 | semidirect |
| 15. #19149658 | C22 | semidirect |
| 16. C2×C4⋊Dic173 | C22 | semidirect |
| 19. #19149610 | C22 | semidirect |
| 20. #19149602 | C22 | semidirect |
| 21. #19149600 | C22 | semidirect |
| 23. C22⋊#13063436 | C22 | semidirect |
| 80. C23×C173 | SD16 | semidirect |
| 129. C173 | #3187 | semidirect |
| 203. C23 | #14583814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149658 | 2 |
| #26011821 | 2 |
| #26011807 | 2 |
| #26011718 | 2 |
| #26011642 | 2 |
| #26011629 | 2 |
| C2×C22⋊#13063436 | 2 |
| C2×#121×C173 | 2 |
| #3187 | 173 |