Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14583816 | C2 | semidirect |
| 2. C22×#14583815 | C2 | semidirect |
| 4. C2×#19149668 | C2 | semidirect |
| 5. C2×#19149666 | C2 | semidirect |
| 6. #26011872 | C2 | direct (N × H) |
| 7. C2×C8×Dic173 | C2 | semidirect |
| 8. C22×SD16×C173 | C2 | semidirect |
| 12. C2×#14583816 | C22 | semidirect |
| 14. C2×#14583815 | C22 | semidirect |
| 19. #19149668 | C22 | semidirect |
| 21. #19149666 | C22 | semidirect |
| 25. C8×Dic173 | C22 | semidirect |
| 29. C2×SD16×C173 | C22 | semidirect |
| 112. C2×C173 | #495 | semidirect |
| 116. C173 | C2×#495 | semidirect |
| 120. C22×SD16 | D173 | semidirect |
| 135. C2×SD16 | C2×D173 | semidirect |
| 230. C2 | #26011872 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583816 | 2 |
| C22×#14583815 | 2 |
| C22×#14583811 | 2 |
| C2×#19149668 | 2 |
| C2×#19149666 | 2 |
| #26011872 | 2 |
| C2×C8×Dic173 | 2 |
| C22×SD16×C173 | 2 |
| C2×#495 | 173 |