Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. #26011831 | C2 | semidirect |
| 4. #26011830 | C2 | semidirect |
| 5. #26011825 | C2 | semidirect |
| 6. #26011820 | C2 | semidirect |
| 7. #26011534 | C2 | semidirect |
| 8. #26011533 | C2 | semidirect |
| 9. #26011500 | C2 | semidirect |
| 11. #419×C173 | C2 | semidirect |
| 30. #19149613 | C22 | semidirect |
| 31. #19149612 | C22 | semidirect |
| 32. #19149611 | C22 | semidirect |
| 33. #19149610 | C22 | semidirect |
| 34. #19149603 | C22 | semidirect |
| 35. #19149603 | C22 | semidirect |
| 41. #103×C173 | C22 | semidirect |
| 42. #103×C173 | C22 | semidirect |
| 146. C173 | #3095 | semidirect |
| 157. #419 | D173 | semidirect |
| 186. #103 | C2×D173 | semidirect |
| 187. #103 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149655 | 2 |
| #117×D173 | 2 |
| #26011831 | 2 |
| #26011830 | 2 |
| #26011825 | 2 |
| #26011820 | 2 |
| #26011534 | 2 |
| #26011533 | 2 |
| #26011500 | 2 |
| #26011454 | 2 |
| #419×C173 | 2 |
| #3095 | 173 |