Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
414 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 2. #26011829 | C2 | semidirect |
| 3. #26011826 | C2 | semidirect |
| 4. #26011809 | C2 | semidirect |
| 5. #26011747 | C2 | semidirect |
| 6. #26011739 | C2 | semidirect |
| 7. #26011651 | C2 | semidirect |
| 8. #26011647 | C2 | semidirect |
| 9. #26011630 | C2 | semidirect |
| 10. #26011455 | C2 | semidirect |
| 11. C2×C22⋊Q8×C173 | C2 | semidirect |
| 13. C2×#14583816 | C22 | semidirect |
| 14. C2×#14583813 | C22 | semidirect |
| 25. #19149612 | C22 | semidirect |
| 26. #19149610 | C22 | semidirect |
| 27. #19149603 | C22 | semidirect |
| 28. #19149603 | C22 | semidirect |
| 29. #19149602 | C22 | semidirect |
| 30. #19149599 | C22 | semidirect |
| 149. C173 | #3196 | semidirect |
| 152. C2×C22⋊Q8 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012002 | 2 |
| #26011829 | 2 |
| #26011826 | 2 |
| #26011809 | 2 |
| #26011747 | 2 |
| #26011739 | 2 |
| #26011651 | 2 |
| #26011647 | 2 |
| #26011630 | 2 |
| #26011455 | 2 |
| C2×C22⋊Q8×C173 | 2 |
| #3196 | 173 |