Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#19149655 | C2 | semidirect |
| 3. #26011831 | C2 | semidirect |
| 4. #26011827 | C2 | semidirect |
| 5. #26011807 | C2 | semidirect |
| 6. #26011748 | C2 | semidirect |
| 7. #26011734 | C2 | semidirect |
| 8. #26011650 | C2 | semidirect |
| 9. #26011647 | C2 | semidirect |
| 10. #26011453 | C2 | semidirect |
| 11. #448×C173 | C2 | semidirect |
| 14. C2×#14583816 | C22 | semidirect |
| 31. #19149613 | C22 | semidirect |
| 32. #19149610 | C22 | semidirect |
| 33. #19149604 | C22 | semidirect |
| 34. #19149603 | C22 | semidirect |
| 35. #19149600 | C22 | semidirect |
| 39. C2×SD16×C173 | C22 | semidirect |
| 41. #103×C173 | C22 | semidirect |
| 149. C173 | #3196 | semidirect |
| 160. #448 | D173 | semidirect |
| 166. C2×SD16 | C2×D173 | semidirect |
| 188. #103 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012001 | 2 |
| C2×#19149655 | 2 |
| #26011831 | 2 |
| #26011827 | 2 |
| #26011807 | 2 |
| #26011748 | 2 |
| #26011734 | 2 |
| #26011650 | 2 |
| #26011647 | 2 |
| #26011453 | 2 |
| #448×C173 | 2 |
| #3196 | 173 |