Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14583813 | C2 | semidirect |
| 3. C2×#19149668 | C2 | semidirect |
| 4. C2×#19149641 | C2 | semidirect |
| 5. #26011709 | C2 | direct (N × H) |
| 6. C2×#19149608 | C2 | semidirect |
| 7. C2×#19149599 | C2 | semidirect |
| 8. C2×#103×C173 | C2 | semidirect |
| 13. C2×#14583813 | C22 | semidirect |
| 18. #19149668 | C22 | semidirect |
| 20. #19149641 | C22 | semidirect |
| 25. #19149608 | C22 | semidirect |
| 26. #19149599 | C22 | semidirect |
| 30. #103×C173 | C22 | semidirect |
| 117. C2×C173 | #463 | semidirect |
| 123. C173 | C2×#463 | semidirect |
| 131. C2×#103 | D173 | semidirect |
| 153. #103 | C2×D173 | semidirect |
| 243. C2 | #26011709 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583813 | 2 |
| C22×D1384 | 2 |
| C2×#19149668 | 2 |
| C2×#19149641 | 2 |
| #26011709 | 2 |
| C2×#19149608 | 2 |
| C2×#19149599 | 2 |
| C2×#103×C173 | 2 |
| C2×#463 | 173 |