Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26011519 | C2 | semidirect |
| 5. #26011252 | C2 | semidirect |
| 6. #26011245 | C2 | semidirect |
| 7. C2×#108×C173 | C2 | semidirect |
| 19. #19149604 | C4 | semidirect |
| 20. #19149604 | C4 | semidirect |
| 21. #19149601 | C4 | semidirect |
| 22. #19149601 | C4 | semidirect |
| 109. C173 | #1866 | semidirect |
| 112. C2×#108 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149687 | 2 |
| #26011519 | 2 |
| C2×#19149605 | 2 |
| #26011488 | 2 |
| #26011252 | 2 |
| #26011245 | 2 |
| C2×#108×C173 | 2 |
| #1866 | 173 |