Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
300 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #26011446 | C2 | semidirect |
| 4. C2×C8×Dic173 | C2 | semidirect |
| 5. #26011255 | C2 | semidirect |
| 6. #26011252 | C2 | semidirect |
| 12. #19149606 | C4 | semidirect |
| 13. #19149603 | C4 | semidirect |
| 14. #19149600 | C4 | semidirect |
| 20. #131×C173 | C4 | semidirect |
| 98. C173 | #1764 | semidirect |
| 109. #131 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149606 | 2 |
| #26011487 | 2 |
| #26011446 | 2 |
| C2×C8×Dic173 | 2 |
| #26011255 | 2 |
| #26011252 | 2 |
| C2×#131×C173 | 2 |
| #1764 | 173 |