Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 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×#14583813 | C2 | semidirect |
| 2. C22×D1384 | C2 | semidirect |
| 3. C22×#14583811 | C2 | semidirect |
| 4. C2×#19149675 | C2 | semidirect |
| 5. C2×#19149668 | C2 | semidirect |
| 6. #26011877 | C2 | direct (N × H) |
| 7. C2×#19149589 | C2 | semidirect |
| 8. C22×SD16×C173 | C2 | semidirect |
| 13. C2×#14583813 | C22 | semidirect |
| 15. C2×D1384 | C22 | semidirect |
| 17. C2×#14583811 | C22 | semidirect |
| 20. #19149675 | C22 | semidirect |
| 22. #19149668 | C22 | semidirect |
| 25. #19149589 | C22 | semidirect |
| 29. C2×SD16×C173 | C22 | semidirect |
| 47. C2×#13063436 | D4 | semidirect |
| 64. C2×C8×C173 | D4 | semidirect |
| 81. #13063436 | C2×D4 | semidirect |
| 98. C8×C173 | C2×D4 | semidirect |
| 117. C2×C173 | #496 | semidirect |
| 122. C173 | C2×#496 | semidirect |
| 125. C22×SD16 | D173 | semidirect |
| 140. C2×SD16 | C2×D173 | semidirect |
| 184. C2×C8 | C22⋊D173 | semidirect |
| 221. C8 | C2×C22⋊D173 | semidirect |
| 242. C2 | #26011877 | 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 |
| C22×#14583811 | 2 |
| C2×#19149675 | 2 |
| C2×#19149668 | 2 |
| #26011877 | 2 |
| C2×#19149589 | 2 |
| C22×SD16×C173 | 2 |
| C2×#496 | 173 |