Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26012002 | C2 | semidirect |
| 2. #26011833 | C2 | semidirect |
| 3. #26011816 | C2 | semidirect |
| 4. #26011732 | C2 | semidirect |
| 5. #26011727 | C2 | semidirect |
| 6. #26011720 | C2 | semidirect |
| 7. #26011655 | C2 | semidirect |
| 8. #26011638 | C2 | semidirect |
| 9. C2×C22⋊C8×C173 | C2 | semidirect |
| 11. C2×Dic692 | C22 | semidirect |
| 12. C2×#14583815 | C22 | semidirect |
| 13. C2×D1384 | C22 | semidirect |
| 23. #19149613 | C22 | semidirect |
| 24. #19149613 | C22 | semidirect |
| 25. #19149611 | C22 | semidirect |
| 26. #19149604 | C22 | semidirect |
| 27. #19149604 | C22 | semidirect |
| 28. #19149601 | C22 | semidirect |
| 29. #19149601 | C22 | semidirect |
| 121. C173 | #3191 | semidirect |
| 131. C2×C22⋊C8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012002 | 2 |
| #26011833 | 2 |
| #26011816 | 2 |
| #26011732 | 2 |
| #26011727 | 2 |
| #26011720 | 2 |
| #26011655 | 2 |
| #26011638 | 2 |
| C2×C22⋊C8×C173 | 2 |
| #3191 | 173 |