Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #26012299 | C2 | semidirect |
| 2. #26012293 | C2 | semidirect |
| 3. #26011876 | C2 | semidirect |
| 4. #26011763 | C2 | semidirect |
| 5. #26011761 | C2 | semidirect |
| 6. #26011756 | C2 | semidirect |
| 7. #26011667 | C2 | semidirect |
| 8. #26011664 | C2 | semidirect |
| 9. #26011608 | C2 | semidirect |
| 10. #26011606 | C2 | semidirect |
| 11. #578×C173 | C2 | semidirect |
| 18. #19149704 | C22 | semidirect |
| 23. C2×#14583813 | C22 | semidirect |
| 26. #19149686 | C22 | semidirect |
| 28. #19149668 | C22 | semidirect |
| 29. #19149615 | C22 | semidirect |
| 30. #19149614 | C22 | semidirect |
| 31. #19149606 | C22 | semidirect |
| 32. #19149606 | C22 | semidirect |
| 34. #19149598 | C22 | semidirect |
| 35. #19149595 | C22 | semidirect |
| 36. C8×Dic173 | C22 | semidirect |
| 37. 2−1+4×C173 | C22 | semidirect |
| 39. #137×C173 | C22 | semidirect |
| 43. C2×Q16×C173 | C22 | semidirect |
| 44. #131×C173 | C22 | semidirect |
| 149. C173 | #3290 | semidirect |
| 151. #578 | D173 | semidirect |
| 162. 2−1+4 | C2×D173 | semidirect |
| 167. #137 | C2×D173 | semidirect |
| 178. C2×Q16 | C2×D173 | semidirect |
| 185. #131 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012299 | 2 |
| #26012293 | 2 |
| #26011876 | 2 |
| #26011763 | 2 |
| #26011761 | 2 |
| #26011756 | 2 |
| #26011667 | 2 |
| #26011664 | 2 |
| #26011608 | 2 |
| #26011606 | 2 |
| #578×C173 | 2 |
| #3290 | 173 |