Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26011829 | C2 | semidirect |
| 3. #26011788 | C2 | semidirect |
| 4. #26011693 | C2 | semidirect |
| 6. #26011589 | C2 | semidirect |
| 7. C4×#14583813 | C2 | semidirect |
| 8. #26011552 | C2 | semidirect |
| 9. #541×C173 | C2 | semidirect |
| 18. #19149612 | C22 | semidirect |
| 19. #19149610 | C22 | semidirect |
| 20. C4⋊#13063436 | C22 | semidirect |
| 21. #19149603 | C22 | semidirect |
| 22. #19149603 | C22 | semidirect |
| 26. #19149590 | C22 | semidirect |
| 27. C4×#13063436 | C22 | semidirect |
| 28. C4⋊Q8×C173 | C22 | semidirect |
| 31. #125×C173 | C22 | semidirect |
| 33. C4×Q8×C173 | C22 | semidirect |
| 102. C173 | #3123 | semidirect |
| 104. #541 | D173 | semidirect |
| 116. C4⋊Q8 | C2×D173 | semidirect |
| 119. #125 | C2×D173 | semidirect |
| 121. C4×Q8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011965 | 2 |
| #26011829 | 2 |
| #26011788 | 2 |
| #26011693 | 2 |
| #26011641 | 2 |
| #26011589 | 2 |
| C4×#14583813 | 2 |
| #26011552 | 2 |
| #541×C173 | 2 |
| #3123 | 173 |