Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19149726 | C2 | semidirect |
| 2. #26012289 | C2 | semidirect |
| 3. #26012062 | C2 | semidirect |
| 4. #26011672 | C2 | semidirect |
| 5. #26011662 | C2 | semidirect |
| 6. #26011508 | C2 | semidirect |
| 7. #26011507 | C2 | semidirect |
| 8. C2×#19149597 | C2 | semidirect |
| 9. #575×C173 | C2 | semidirect |
| 21. #19149710 | C22 | semidirect |
| 23. #19149705 | C22 | semidirect |
| 27. #19149677 | C22 | semidirect |
| 28. #19149666 | C22 | semidirect |
| 32. #19149606 | C22 | semidirect |
| 33. #19149605 | C22 | semidirect |
| 34. #19149597 | C22 | semidirect |
| 38. #137×C173 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C173 | C22 | semidirect |
| 185. C173 | #3020 | semidirect |
| 189. #575 | D173 | semidirect |
| 212. #137 | C2×D173 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149726 | 2 |
| #26012289 | 2 |
| #26012062 | 2 |
| #26011672 | 2 |
| #26011662 | 2 |
| #26011508 | 2 |
| #26011507 | 2 |
| C2×#19149597 | 2 |
| #575×C173 | 2 |
| #3020 | 173 |