Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26011857 | C2 | semidirect |
| 3. #26011853 | C2 | semidirect |
| 4. #26011848 | C2 | semidirect |
| 5. #26011839 | C2 | semidirect |
| 6. #26011495 | C2 | semidirect |
| 7. #26011490 | C2 | semidirect |
| 8. #26011485 | C2 | semidirect |
| 9. C2×#19149599 | C2 | semidirect |
| 10. #26011447 | C2 | semidirect |
| 11. #544×C173 | C2 | semidirect |
| 21. #19149602 | C22 | semidirect |
| 22. #19149602 | C22 | semidirect |
| 23. #19149602 | C22 | semidirect |
| 28. #19149599 | C22 | semidirect |
| 29. #19149599 | C22 | semidirect |
| 30. #19149599 | C22 | semidirect |
| 31. #19149590 | C22 | semidirect |
| 32. C4×#13063436 | C22 | semidirect |
| 34. C4⋊Q8×C173 | C22 | semidirect |
| 36. #125×C173 | C22 | semidirect |
| 135. C173 | #3136 | semidirect |
| 137. #544 | D173 | semidirect |
| 153. C4⋊Q8 | C2×D173 | semidirect |
| 156. #125 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012060 | 2 |
| #26011857 | 2 |
| #26011853 | 2 |
| #26011848 | 2 |
| #26011839 | 2 |
| #26011495 | 2 |
| #26011490 | 2 |
| #26011485 | 2 |
| C2×#19149599 | 2 |
| #26011447 | 2 |
| #544×C173 | 2 |
| #3136 | 173 |