Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
368 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 69 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×#19149594 | C2 | semidirect |
| 3. #26011283 | C2 | direct (N × H) |
| 4. C2×#99×C173 | C2 | semidirect |
| 5. C22×D692 | C4 | semidirect |
| 10. #19149675 | C4 | semidirect |
| 13. C2×C4×Dic173 | C4 | semidirect |
| 15. #19149594 | C22 | semidirect |
| 19. #99×C173 | C22 | semidirect |
| 24. C2×D692 | C2×C4 | semidirect |
| 36. C4×Dic173 | C2×C4 | semidirect |
| 117. C2×C173 | #353 | semidirect |
| 120. C173 | C2×#353 | semidirect |
| 124. C2×#99 | D173 | semidirect |
| 140. #99 | C2×D173 | semidirect |
| 239. C2 | #26011283 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149675 | 2 |
| C2×#19149594 | 2 |
| #26011283 | 2 |
| C2×#99×C173 | 2 |
| C2×#353 | 173 |