Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 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×C8×D173 | C2 | semidirect |
| 2. C2×#19149655 | C2 | semidirect |
| 4. #26011717 | C2 | direct (N × H) |
| 5. C2×#19149611 | C2 | semidirect |
| 6. C2×#19149603 | C2 | semidirect |
| 7. C2×#19149600 | C2 | semidirect |
| 8. C22×SD16×C173 | C2 | semidirect |
| 13. C2×C8×D173 | C22 | semidirect |
| 15. #19149655 | C22 | semidirect |
| 23. #19149611 | C22 | semidirect |
| 24. #19149603 | C22 | semidirect |
| 25. #19149600 | C22 | semidirect |
| 29. C2×SD16×C173 | C22 | semidirect |
| 63. C2×C8×C173 | D4 | semidirect |
| 67. C22×D173 | SD16 | semidirect |
| 97. C8×C173 | C2×D4 | semidirect |
| 109. C2×D173 | C2×SD16 | semidirect |
| 118. C2×C173 | #465 | semidirect |
| 123. C173 | C2×#465 | semidirect |
| 125. C22×SD16 | D173 | semidirect |
| 138. C2×SD16 | C2×D173 | semidirect |
| 180. C2×C8 | C22⋊D173 | semidirect |
| 221. C8 | C2×C22⋊D173 | semidirect |
| 243. C2 | #26011717 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D173 | 2 |
| C2×#19149655 | 2 |
| C2×#19149650 | 2 |
| #26011717 | 2 |
| C2×#19149611 | 2 |
| C2×#19149603 | 2 |
| C2×#19149600 | 2 |
| C22×SD16×C173 | 2 |
| C2×#465 | 173 |