Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14583814 | C2 | semidirect |
| 3. #26012067 | C2 | semidirect |
| 4. #26011706 | C2 | semidirect |
| 5. #26011696 | C2 | semidirect |
| 6. #26011518 | C2 | semidirect |
| 7. #26011499 | C2 | semidirect |
| 8. #26011485 | C2 | semidirect |
| 9. #518×C173 | C2 | semidirect |
| 19. #19149679 | C22 | semidirect |
| 20. #19149667 | C22 | semidirect |
| 23. C4⋊#13063436 | C22 | semidirect |
| 24. #19149602 | C22 | semidirect |
| 25. #19149602 | C22 | semidirect |
| 26. #19149599 | C22 | semidirect |
| 116. C173 | #3042 | semidirect |
| 121. #518 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149705 | 2 |
| C22×#14583814 | 2 |
| #26012067 | 2 |
| #26011706 | 2 |
| #26011696 | 2 |
| #26011518 | 2 |
| #26011499 | 2 |
| #26011485 | 2 |
| #518×C173 | 2 |
| #3042 | 173 |