Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012122 | C2 | semidirect |
| 3. #26011854 | C2 | semidirect |
| 4. #26011852 | C2 | semidirect |
| 5. #26011847 | C2 | semidirect |
| 6. #26011836 | C2 | semidirect |
| 7. #26011497 | C2 | semidirect |
| 8. #26011487 | C2 | semidirect |
| 9. C2×#19149599 | C2 | semidirect |
| 10. #26011449 | C2 | semidirect |
| 11. #417×C173 | C2 | semidirect |
| 15. #19149678 | C22 | semidirect |
| 18. #19149670 | C22 | semidirect |
| 26. #19149603 | C22 | semidirect |
| 27. #19149603 | C22 | semidirect |
| 30. #19149600 | C22 | semidirect |
| 31. #19149600 | C22 | semidirect |
| 34. #19149589 | C22 | semidirect |
| 35. C8×Dic173 | C22 | semidirect |
| 39. #103×C173 | C22 | semidirect |
| 40. #102×C173 | C22 | semidirect |
| 135. C173 | #3136 | semidirect |
| 144. #417 | D173 | semidirect |
| 167. #103 | C2×D173 | semidirect |
| 174. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012122 | 2 |
| #26012055 | 2 |
| #26011854 | 2 |
| #26011852 | 2 |
| #26011847 | 2 |
| #26011836 | 2 |
| #26011497 | 2 |
| #26011487 | 2 |
| C2×#19149599 | 2 |
| #26011449 | 2 |
| #417×C173 | 2 |
| #3136 | 173 |