Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #26011971 | C2 | semidirect |
| 3. #26011814 | C2 | semidirect |
| 4. #26011813 | C2 | semidirect |
| 5. #26011808 | C2 | semidirect |
| 6. #26011803 | C2 | semidirect |
| 7. #26011533 | C2 | semidirect |
| 8. #26011527 | C2 | semidirect |
| 9. C2×#19149600 | C2 | semidirect |
| 10. #26011459 | C2 | semidirect |
| 11. #418×C173 | C2 | semidirect |
| 23. #19149637 | C22 | semidirect |
| 25. C4⋊C4×D173 | C22 | semidirect |
| 26. #19149613 | C22 | semidirect |
| 27. #19149612 | C22 | semidirect |
| 28. #19149612 | C22 | semidirect |
| 29. #19149611 | C22 | semidirect |
| 30. #19149610 | C22 | semidirect |
| 31. #19149610 | C22 | semidirect |
| 34. #19149591 | C22 | semidirect |
| 35. #19149591 | C22 | semidirect |
| 134. C173 | #3096 | semidirect |
| 144. #418 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012058 | 2 |
| #26011971 | 2 |
| #26011814 | 2 |
| #26011813 | 2 |
| #26011808 | 2 |
| #26011803 | 2 |
| #26011533 | 2 |
| #26011527 | 2 |
| C2×#19149600 | 2 |
| #26011459 | 2 |
| #418×C173 | 2 |
| #3096 | 173 |