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. #26011382 | C2 | semidirect |
| 4. #26011381 | C2 | semidirect |
| 5. #26011379 | C2 | semidirect |
| 6. #26011371 | C2 | semidirect |
| 7. #26011368 | C2 | semidirect |
| 8. #26011346 | C2 | semidirect |
| 9. #390×C173 | C2 | semidirect |
| 12. C23×Dic173 | C22 | semidirect |
| 13. #19149647 | C4 | semidirect |
| 14. C2×#14583805 | C22 | semidirect |
| 17. C2×C22⋊Dic173 | C22 | semidirect |
| 23. C2×C4×Dic173 | C22 | semidirect |
| 24. #19149586 | C22 | semidirect |
| 25. #19149586 | C22 | semidirect |
| 26. #19149586 | C22 | semidirect |
| 28. C2×C4⋊C4×C173 | C22 | semidirect |
| 30. C2×C22⋊C4×C173 | C22 | semidirect |
| 31. C2×C42×C173 | C22 | semidirect |
| 36. C23×D173 | C2×C4 | semidirect |
| 49. C22⋊Dic173 | C2×C4 | semidirect |
| 54. #14583803 | C2×C4 | semidirect |
| 149. C173 | #2375 | semidirect |
| 153. #390 | D173 | semidirect |
| 166. C2×C4⋊C4 | C2×D173 | semidirect |
| 176. C2×C22⋊C4 | C2×D173 | semidirect |
| 178. C2×C42 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149647 | 2 |
| #26011391 | 2 |
| #26011382 | 2 |
| #26011381 | 2 |
| #26011379 | 2 |
| #26011371 | 2 |
| #26011368 | 2 |
| #26011346 | 2 |
| #390×C173 | 2 |
| #2375 | 173 |