Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
680 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 338 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. C2×#19149733 | C2 | direct (N × H) |
| 6. C2×D173⋊C8 | C4 | semidirect |
| 8. C22×#13063443 | C4 | semidirect |
| 11. #19149733 | C22 | direct (N × H) |
| 13. C22×#13063436 | C4 | semidirect |
| 14. C2×C8×D173 | C4 | semidirect |
| 16. C22×C8×C173 | C4 | semidirect |
| 19. D173⋊C8 | C2×C4 | semidirect |
| 21. C2×#13063443 | C2×C4 | semidirect |
| 30. C2×#13063436 | C2×C4 | semidirect |
| 31. C8×D173 | C2×C4 | semidirect |
| 34. C2×C8×C173 | C2×C4 | semidirect |
| 37. #13063443 | C22×C4 | semidirect |
| 48. #13063436 | C22×C4 | semidirect |
| 52. C8×C173 | C22×C4 | semidirect |
| 53. C22×C173 | #97 | semidirect |
| 55. C2×D173 | #97 | semidirect |
| 64. C2×C173 | C2×#97 | semidirect |
| 66. D173 | C2×#97 | semidirect |
| 68. C173 | C22×#97 | semidirect |
| 82. C22×C8 | #10621924 | semidirect |
| 101. C2×C8 | C2×#10621924 | semidirect |
| 121. C8 | C22×#10621924 | semidirect |
| 126. C22 | #19149733 | direct (N × H) |
| 135. C2 | C2×#19149733 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D173⋊C8 | 2 |
| C22×C4×#10621924 | 2 |
| C2×#19149733 | 2 |
| C22×C8×D173 | 2 |
| C22×#97 | 173 |