Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149701 | C2 | semidirect |
| 2. #26012002 | C2 | semidirect |
| 3. #26011749 | C2 | semidirect |
| 4. #26011744 | C2 | semidirect |
| 5. #26011737 | C2 | semidirect |
| 6. #26011529 | C2 | semidirect |
| 7. #26011488 | C2 | semidirect |
| 8. C22×M16×C173 | C2 | semidirect |
| 11. C2×Dic692 | C22 | semidirect |
| 12. C2×#14583815 | C22 | semidirect |
| 13. C2×D1384 | C22 | semidirect |
| 20. #19149613 | C22 | semidirect |
| 21. #19149611 | C22 | semidirect |
| 22. #19149604 | C22 | semidirect |
| 23. #19149601 | C22 | semidirect |
| 56. C2×C8×C173 | D4 | semidirect |
| 105. C173 | #3054 | semidirect |
| 108. C22×M16 | D173 | semidirect |
| 156. C2×C8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| #26012002 | 2 |
| #26011749 | 2 |
| #26011744 | 2 |
| #26011737 | 2 |
| #26011529 | 2 |
| #26011488 | 2 |
| C22×M16×C173 | 2 |
| #3054 | 173 |