Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
512 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 269 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. #26011527 | C2 | direct (N × H) |
| 4. C2×#19149612 | C2 | semidirect |
| 5. C2×#19149610 | C2 | semidirect |
| 7. C22×#13063436 | C4 | semidirect |
| 16. #19149612 | C22 | semidirect |
| 17. #19149610 | C22 | semidirect |
| 27. C2×#13063436 | C2×C4 | semidirect |
| 78. C2×C173 | #427 | semidirect |
| 81. C173 | C2×#427 | semidirect |
| 160. C2 | #26011527 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13063436 | 2 |
| C2×#19149638 | 2 |
| #26011527 | 2 |
| C2×#19149612 | 2 |
| C2×#19149610 | 2 |
| C2×#117×C173 | 2 |
| C2×#427 | 173 |