Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19149586 | C2 | semidirect |
| 3. #26011226 | C2 | direct (N × H) |
| 4. C2×C22⋊C8×C173 | C2 | semidirect |
| 5. C22×D692 | C4 | semidirect |
| 10. #19149653 | C4 | semidirect |
| 12. C2×C4⋊Dic173 | C4 | semidirect |
| 15. #19149586 | C22 | semidirect |
| 19. C22⋊C8×C173 | C22 | semidirect |
| 23. C2×D692 | C2×C4 | semidirect |
| 34. C4⋊Dic173 | C2×C4 | semidirect |
| 106. C2×C173 | #327 | semidirect |
| 111. C173 | C2×#327 | semidirect |
| 114. C2×C22⋊C8 | D173 | semidirect |
| 129. C22⋊C8 | C2×D173 | semidirect |
| 219. C2 | #26011226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149653 | 2 |
| C2×#19149586 | 2 |
| #26011226 | 2 |
| C2×C22⋊C8×C173 | 2 |
| C2×#327 | 173 |