Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26011788 | C2 | semidirect |
| 3. #26011788 | C2 | semidirect |
| 4. #26011778 | C2 | semidirect |
| 5. #26011768 | C2 | semidirect |
| 6. #26011531 | C2 | semidirect |
| 7. #26011527 | C2 | semidirect |
| 8. #26011518 | C2 | semidirect |
| 11. #544×C173 | C2 | semidirect |
| 21. #19149612 | C22 | semidirect |
| 22. #19149612 | C22 | semidirect |
| 23. #19149612 | C22 | semidirect |
| 24. #19149610 | C22 | semidirect |
| 25. #19149610 | C22 | semidirect |
| 26. #19149610 | C22 | semidirect |
| 27. C4⋊#13063436 | C22 | semidirect |
| 28. C4⋊#13063436 | C22 | semidirect |
| 34. C4⋊Q8×C173 | C22 | semidirect |
| 36. #125×C173 | C22 | semidirect |
| 44. C2×D692 | Q8 | semidirect |
| 124. C173 | #3081 | semidirect |
| 126. #544 | D173 | semidirect |
| 141. C4⋊Q8 | C2×D173 | semidirect |
| 143. #125 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011965 | 2 |
| #26011788 | 2 |
| #26011778 | 2 |
| #26011768 | 2 |
| #26011531 | 2 |
| #26011527 | 2 |
| #26011518 | 2 |
| #26011495 | 2 |
| C2×#19149599 | 2 |
| #544×C173 | 2 |
| #3081 | 173 |