Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
648 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 648 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×#14583811 | C2 | semidirect |
| 2. C2×#19149675 | C2 | semidirect |
| 3. C2×D4×Dic173 | C2 | semidirect |
| 4. #26011684 | C2 | direct (N × H) |
| 5. C2×#19149608 | C2 | semidirect |
| 6. C2×#19149601 | C2 | semidirect |
| 7. C2×#19149600 | C2 | semidirect |
| 8. C22×D8×C173 | C2 | semidirect |
| 14. C2×#14583811 | C22 | semidirect |
| 17. #19149675 | C22 | semidirect |
| 19. D4×Dic173 | C22 | semidirect |
| 23. #19149608 | C22 | semidirect |
| 24. #19149601 | C22 | semidirect |
| 25. #19149600 | C22 | semidirect |
| 29. C2×D8×C173 | C22 | semidirect |
| 60. C2×D4×C173 | D4 | semidirect |
| 80. C2×Dic173 | D8 | semidirect |
| 98. D4×C173 | C2×D4 | semidirect |
| 125. Dic173 | C2×D8 | semidirect |
| 128. C2×C173 | #459 | semidirect |
| 133. C173 | C2×#459 | semidirect |
| 136. C22×D8 | D173 | semidirect |
| 152. C2×D8 | C2×D173 | semidirect |
| 181. C2×D4 | C22⋊D173 | semidirect |
| 224. D4 | C2×C22⋊D173 | semidirect |
| 263. C2 | #26011684 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583811 | 2 |
| C2×#19149675 | 2 |
| C2×D4×Dic173 | 2 |
| #26011684 | 2 |
| C2×#19149608 | 2 |
| C2×#19149601 | 2 |
| C2×#19149600 | 2 |
| C22×D8×C173 | 2 |
| C2×#459 | 173 |