Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
156 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26011318 | C2 | semidirect |
| 4. #26011316 | C2 | semidirect |
| 7. #19149619 | C4 | semidirect |
| 19. #14583801 | C2×C4 | semidirect |
| 55. C173 | #2159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149619 | 2 |
| C2×#19149613 | 2 |
| #26011318 | 2 |
| #26011316 | 2 |
| #427×C173 | 2 |
| #2159 | 173 |