Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19149705 | C2 | semidirect |
| 3. C2×#19149666 | C2 | semidirect |
| 4. #26011662 | C2 | direct (N × H) |
| 5. C2×#19149606 | C2 | semidirect |
| 6. C2×#19149605 | C2 | semidirect |
| 7. C2×#19149597 | C2 | semidirect |
| 8. C2×AGL(1,ℤ/8)×C173 | C2 | semidirect |
| 12. #19149726 | C22 | semidirect |
| 21. #19149705 | C22 | semidirect |
| 26. #19149666 | C22 | semidirect |
| 29. #19149606 | C22 | semidirect |
| 30. #19149605 | C22 | semidirect |
| 31. #19149597 | C22 | semidirect |
| 35. AGL(1,ℤ/8)×C173 | C22 | semidirect |
| 172. C2×C173 | #454 | semidirect |
| 175. C173 | C2×#454 | semidirect |
| 179. C2×AGL(1,ℤ/8) | D173 | semidirect |
| 201. AGL(1,ℤ/8) | C2×D173 | semidirect |
| 349. C2 | #26011662 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149726 | 2 |
| C2×#19149705 | 2 |
| C2×#19149666 | 2 |
| #26011662 | 2 |
| C2×#19149606 | 2 |
| C2×#19149605 | 2 |
| C2×#19149597 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| C2×#454 | 173 |