Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
528 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#19149678 | C2 | semidirect |
| 3. #26011836 | C2 | direct (N × H) |
| 4. C2×#19149601 | C2 | semidirect |
| 5. C2×#19149600 | C2 | semidirect |
| 6. C2×#19149599 | C2 | semidirect |
| 7. C2×C8×Dic173 | C2 | semidirect |
| 8. C2×#102×C173 | C2 | semidirect |
| 15. #19149678 | C22 | semidirect |
| 21. #19149601 | C22 | semidirect |
| 22. #19149600 | C22 | semidirect |
| 23. #19149599 | C22 | semidirect |
| 24. C8×Dic173 | C22 | semidirect |
| 28. #102×C173 | C22 | semidirect |
| 113. C2×C173 | #486 | semidirect |
| 118. C173 | C2×#486 | semidirect |
| 126. C2×#102 | D173 | semidirect |
| 146. #102 | C2×D173 | semidirect |
| 233. C2 | #26011836 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149678 | 2 |
| C2×#19149675 | 2 |
| #26011836 | 2 |
| C2×#19149601 | 2 |
| C2×#19149600 | 2 |
| C2×#19149599 | 2 |
| C2×C8×Dic173 | 2 |
| C2×#102×C173 | 2 |
| C2×#486 | 173 |