Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 1. #26012046 | C2 | semidirect |
| 3. #26011853 | C2 | semidirect |
| 4. #26011851 | C2 | semidirect |
| 5. #26011850 | C2 | semidirect |
| 6. #26011847 | C2 | semidirect |
| 7. #26011844 | C2 | semidirect |
| 8. #26011498 | C2 | semidirect |
| 10. #26011443 | C2 | semidirect |
| 11. #489×C173 | C2 | semidirect |
| 15. #19149679 | C22 | semidirect |
| 16. #19149670 | C22 | semidirect |
| 30. #19149604 | C22 | semidirect |
| 31. #19149603 | C22 | semidirect |
| 32. #19149602 | C22 | semidirect |
| 36. #19149590 | C22 | semidirect |
| 37. C8×Dic173 | C22 | semidirect |
| 38. C4⋊Q8×C173 | C22 | semidirect |
| 40. #103×C173 | C22 | semidirect |
| 42. #97×C173 | C22 | semidirect |
| 138. C173 | #3140 | semidirect |
| 145. #489 | D173 | semidirect |
| 155. C4⋊Q8 | C2×D173 | semidirect |
| 174. #103 | C2×D173 | semidirect |
| 180. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| #124×D173 | 2 |
| #26011853 | 2 |
| #26011851 | 2 |
| #26011850 | 2 |
| #26011847 | 2 |
| #26011844 | 2 |
| #26011498 | 2 |
| #26011494 | 2 |
| #26011443 | 2 |
| #489×C173 | 2 |
| #3140 | 173 |