Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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. #26011815 | C2 | semidirect |
| 3. #26011809 | C2 | semidirect |
| 4. #26011804 | C2 | semidirect |
| 5. #26011534 | C2 | semidirect |
| 6. #26011495 | C2 | semidirect |
| 7. #26011455 | C2 | semidirect |
| 8. C2×#117×C173 | C2 | semidirect |
| 18. #19149612 | C22 | semidirect |
| 19. #19149610 | C22 | semidirect |
| 20. #19149599 | C22 | semidirect |
| 21. #19149599 | C22 | semidirect |
| 22. C22⋊#13063436 | C22 | semidirect |
| 23. C22⋊#13063436 | C22 | semidirect |
| 28. #117×C173 | C22 | semidirect |
| 29. C2×C4⋊C4×C173 | C22 | semidirect |
| 30. C2×C4⋊C4×C173 | C22 | semidirect |
| 125. C173 | #3094 | semidirect |
| 128. C2×#117 | D173 | semidirect |
| 146. #117 | C2×D173 | semidirect |
| 148. C2×C4⋊C4 | C2×D173 | semidirect |
| 149. C2×C4⋊C4 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149653 | 2 |
| #26011815 | 2 |
| #26011809 | 2 |
| #26011804 | 2 |
| #26011534 | 2 |
| #26011495 | 2 |
| #26011455 | 2 |
| C2×#117×C173 | 2 |
| #3094 | 173 |