Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012308 | C2 | semidirect |
| 2. #26012301 | C2 | semidirect |
| 3. #26012292 | C2 | semidirect |
| 4. #26011874 | C2 | semidirect |
| 5. #26011767 | C2 | semidirect |
| 6. #26011753 | C2 | semidirect |
| 7. #26011671 | C2 | semidirect |
| 8. #26011662 | C2 | semidirect |
| 9. #26011607 | C2 | semidirect |
| 10. #26011606 | C2 | semidirect |
| 11. #472×C173 | C2 | semidirect |
| 12. #19149726 | C22 | semidirect |
| 16. #19149712 | C22 | semidirect |
| 27. C2×Dic692 | C22 | semidirect |
| 28. C2×#14583814 | C22 | semidirect |
| 31. #19149687 | C22 | semidirect |
| 33. #19149666 | C22 | semidirect |
| 34. #19149614 | C22 | semidirect |
| 35. #19149606 | C22 | semidirect |
| 37. #19149605 | C22 | semidirect |
| 38. #19149597 | C22 | semidirect |
| 39. C8×Dic173 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C173 | C22 | semidirect |
| 42. #131×C173 | C22 | semidirect |
| 43. #108×C173 | C22 | semidirect |
| 44. #100×C173 | C22 | semidirect |
| 149. C173 | #3290 | semidirect |
| 156. #472 | D173 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D173 | semidirect |
| 185. #131 | C2×D173 | semidirect |
| 188. #108 | C2×D173 | semidirect |
| 193. #100 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012308 | 2 |
| #26012301 | 2 |
| #26012292 | 2 |
| #26011874 | 2 |
| #26011767 | 2 |
| #26011753 | 2 |
| #26011671 | 2 |
| #26011662 | 2 |
| #26011607 | 2 |
| #26011606 | 2 |
| #472×C173 | 2 |
| #3290 | 173 |