Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26011449 | C2 | semidirect |
| 4. C2×C4×#13063436 | C2 | semidirect |
| 5. #26011255 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 9. #19149686 | C4 | semidirect |
| 16. #19149603 | C4 | semidirect |
| 17. #19149600 | C4 | semidirect |
| 24. #104×C173 | C4 | semidirect |
| 98. C173 | #1764 | semidirect |
| 118. #104 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149686 | 2 |
| #26011487 | 2 |
| #26011449 | 2 |
| C2×C4×#13063436 | 2 |
| #26011255 | 2 |
| #26011251 | 2 |
| C2×#104×C173 | 2 |
| #1764 | 173 |