Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
792 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×C8×D173 | C2 | semidirect |
| 3. C2×#19149637 | C2 | semidirect |
| 4. #26011486 | C2 | direct (N × H) |
| 5. C2×#19149603 | C2 | semidirect |
| 6. C2×#19149601 | C2 | semidirect |
| 7. C2×#19149599 | C2 | semidirect |
| 8. C2×#103×C173 | C2 | semidirect |
| 11. C2×#14583827 | C4 | semidirect |
| 19. C2×C8×D173 | C22 | semidirect |
| 21. #19149637 | C22 | semidirect |
| 25. #19149603 | C22 | semidirect |
| 26. #19149601 | C22 | semidirect |
| 27. #19149599 | C22 | semidirect |
| 31. #103×C173 | C22 | semidirect |
| 36. #14583827 | C2×C4 | semidirect |
| 122. C2×C173 | #416 | semidirect |
| 128. C173 | C2×#416 | semidirect |
| 135. C2×#103 | D173 | semidirect |
| 158. #103 | C2×D173 | semidirect |
| 253. C2 | #26011486 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583827 | 2 |
| C22×C8×D173 | 2 |
| C2×#19149637 | 2 |
| #26011486 | 2 |
| C2×#19149603 | 2 |
| C2×#19149601 | 2 |
| C2×#19149599 | 2 |
| C2×#103×C173 | 2 |
| C2×#416 | 173 |