Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. #26011519 | C2 | semidirect |
| 4. C2×C4×#13063436 | C2 | semidirect |
| 5. #26011255 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 13. #19149603 | C4 | semidirect |
| 14. #19149600 | C4 | semidirect |
| 90. C173 | #1937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011519 | 2 |
| #26011487 | 2 |
| #26011458 | 2 |
| C2×C4×#13063436 | 2 |
| #26011255 | 2 |
| #26011251 | 2 |
| C2×#104×C173 | 2 |
| #1937 | 173 |