Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26011495 | C2 | semidirect |
| 3. C2×#19149596 | C2 | semidirect |
| 4. #26011250 | C2 | semidirect |
| 5. #518×C173 | C2 | semidirect |
| 10. #19149675 | C4 | semidirect |
| 22. C2×D692 | C2×C4 | semidirect |
| 30. C4×Dic173 | C2×C4 | semidirect |
| 38. C4⋊C4×C173 | D4 | semidirect |
| 87. C173 | #1887 | semidirect |
| 90. #518 | D173 | semidirect |
| 124. C4⋊C4 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149675 | 2 |
| #26011495 | 2 |
| C2×#19149596 | 2 |
| #26011250 | 2 |
| #518×C173 | 2 |
| #1887 | 173 |