Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012025 | C2 | semidirect |
| 2. #26011878 | C2 | semidirect |
| 3. #26011855 | C2 | semidirect |
| 4. #26011688 | C2 | semidirect |
| 5. #26011683 | C2 | semidirect |
| 6. #26011642 | C2 | semidirect |
| 7. #26011625 | C2 | semidirect |
| 8. #26011548 | C2 | semidirect |
| 9. C2×#127×C173 | C2 | semidirect |
| 10. C2×#14583814 | C22 | semidirect |
| 11. C2×#14583811 | C22 | semidirect |
| 13. #19149671 | C22 | semidirect |
| 14. #19149667 | C22 | semidirect |
| 18. C4×Dic346 | C22 | semidirect |
| 19. C4×D692 | C22 | semidirect |
| 22. C4⋊#13063436 | C22 | semidirect |
| 23. #19149600 | C22 | semidirect |
| 24. #19149600 | C22 | semidirect |
| 26. #19149590 | C22 | semidirect |
| 127. C173 | #3217 | semidirect |
| 129. C2×#127 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012025 | 2 |
| #26011878 | 2 |
| #26011855 | 2 |
| #26011688 | 2 |
| #26011683 | 2 |
| #26011642 | 2 |
| #26011625 | 2 |
| #26011548 | 2 |
| C2×#127×C173 | 2 |
| #3217 | 173 |