Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C2×C4×D692 | C2 | semidirect |
| 2. #26011819 | C2 | semidirect |
| 3. #26011802 | C2 | semidirect |
| 4. #26011788 | C2 | semidirect |
| 5. #26011703 | C2 | semidirect |
| 6. #26011641 | C2 | semidirect |
| 8. #26011601 | C2 | semidirect |
| 9. #26011589 | C2 | semidirect |
| 10. #26011548 | C2 | semidirect |
| 11. #529×C173 | C2 | semidirect |
| 22. #19149612 | C22 | semidirect |
| 23. #19149610 | C22 | semidirect |
| 24. C4⋊#13063436 | C22 | semidirect |
| 25. #19149603 | C22 | semidirect |
| 26. #19149600 | C22 | semidirect |
| 31. #19149590 | C22 | semidirect |
| 33. #125×C173 | C22 | semidirect |
| 34. #124×C173 | C22 | semidirect |
| 38. C4×Q8×C173 | C22 | semidirect |
| 40. C4×D4×C173 | C22 | semidirect |
| 140. C173 | #3114 | semidirect |
| 142. #529 | D173 | semidirect |
| 158. #125 | C2×D173 | semidirect |
| 159. #124 | C2×D173 | semidirect |
| 163. C4×Q8 | C2×D173 | semidirect |
| 169. C4×D4 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D692 | 2 |
| #26011819 | 2 |
| #26011802 | 2 |
| #26011788 | 2 |
| #26011703 | 2 |
| #26011641 | 2 |
| #26011624 | 2 |
| #26011601 | 2 |
| #26011589 | 2 |
| #26011548 | 2 |
| #529×C173 | 2 |
| #3114 | 173 |