Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 2. C22×Dic692 | C2 | semidirect |
| 3. C22×#14583815 | C2 | semidirect |
| 4. C2×#19149658 | C2 | semidirect |
| 5. #26011655 | C2 | direct (N × H) |
| 6. C2×#19149604 | C2 | semidirect |
| 7. C2×#19149601 | C2 | semidirect |
| 8. C2×C22⋊C8×C173 | C2 | semidirect |
| 19. C2×Dic692 | C22 | semidirect |
| 21. C2×#14583815 | C22 | semidirect |
| 23. #19149658 | C22 | semidirect |
| 27. #19149604 | C22 | semidirect |
| 28. #19149601 | C22 | semidirect |
| 32. C22⋊C8×C173 | C22 | semidirect |
| 130. C2×C173 | #452 | semidirect |
| 135. C173 | C2×#452 | semidirect |
| 144. C2×C22⋊C8 | D173 | semidirect |
| 168. C22⋊C8 | C2×D173 | semidirect |
| 267. C2 | #26011655 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583826 | 2 |
| C22×Dic692 | 2 |
| C22×#14583815 | 2 |
| C2×#19149658 | 2 |
| #26011655 | 2 |
| C2×#19149604 | 2 |
| C2×#19149601 | 2 |
| C2×C22⋊C8×C173 | 2 |
| C2×#452 | 173 |