Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 536 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. #26011531 | C2 | direct (N × H) |
| 4. C2×#19149612 | C2 | semidirect |
| 5. C2×#19149610 | C2 | semidirect |
| 7. C2×#14583810 | C4 | semidirect |
| 16. #19149612 | C22 | semidirect |
| 17. #19149610 | C22 | semidirect |
| 26. #14583810 | C2×C4 | semidirect |
| 27. C2×#13063436 | C2×C4 | semidirect |
| 52. #13063436 | C22×C4 | semidirect |
| 86. C2×C173 | #428 | semidirect |
| 90. C173 | C2×#428 | semidirect |
| 177. C2 | #26011531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583810 | 2 |
| C2×#19149638 | 2 |
| #26011531 | 2 |
| C2×#19149612 | 2 |
| C2×#19149610 | 2 |
| C22×C4⋊C4×C173 | 2 |
| C2×#428 | 173 |