Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #26011391 | C2 | semidirect |
| 3. #26011385 | C2 | semidirect |
| 4. #26011379 | C2 | semidirect |
| 5. #26011367 | C2 | semidirect |
| 6. #26011347 | C2 | semidirect |
| 7. #379×C173 | C2 | semidirect |
| 9. C22×C4×D173 | C22 | semidirect |
| 10. #19149648 | C4 | semidirect |
| 11. C2×#14583805 | C22 | semidirect |
| 15. C2×#14583803 | C22 | semidirect |
| 16. C2×C4×Dic173 | C22 | semidirect |
| 17. #19149586 | C22 | semidirect |
| 18. #19149586 | C22 | semidirect |
| 33. C22⋊Dic173 | C2×C4 | semidirect |
| 38. C24×C173 | C2×C4 | semidirect |
| 95. C173 | #2375 | semidirect |
| 103. #379 | D173 | semidirect |
| 121. C24 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149648 | 2 |
| #26011391 | 2 |
| #26011385 | 2 |
| #26011379 | 2 |
| #26011367 | 2 |
| #26011347 | 2 |
| #379×C173 | 2 |
| #2375 | 173 |