Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
410 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26011815 | C2 | semidirect |
| 4. #26011739 | C2 | semidirect |
| 5. #26011722 | C2 | semidirect |
| 6. #26011641 | C2 | semidirect |
| 7. #26011630 | C2 | semidirect |
| 8. #26011458 | C2 | semidirect |
| 9. #536×C173 | C2 | semidirect |
| 13. C2×#14583810 | C22 | semidirect |
| 14. C22×#13063436 | C22 | semidirect |
| 22. #19149612 | C22 | semidirect |
| 23. #19149610 | C22 | semidirect |
| 24. #19149603 | C22 | semidirect |
| 25. #19149603 | C22 | semidirect |
| 29. C22⋊#13063436 | C22 | semidirect |
| 31. C22×Q8×C173 | C22 | semidirect |
| 37. C22⋊Q8×C173 | C22 | semidirect |
| 38. #117×C173 | C22 | semidirect |
| 137. C173 | #3200 | semidirect |
| 139. #536 | D173 | semidirect |
| 149. C22×Q8 | C2×D173 | semidirect |
| 162. C22⋊Q8 | C2×D173 | semidirect |
| 168. #117 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012055 | 2 |
| #26011829 | 2 |
| #26011815 | 2 |
| #26011739 | 2 |
| #26011722 | 2 |
| #26011641 | 2 |
| #26011630 | 2 |
| #26011458 | 2 |
| #536×C173 | 2 |
| #3200 | 173 |