Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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. #26012257 | C2 | semidirect |
| 3. #26011475 | C2 | semidirect |
| 4. #26011474 | C2 | semidirect |
| 5. C2×#19149595 | C2 | semidirect |
| 6. #100×D173 | C2 | semidirect |
| 7. #413×C173 | C2 | semidirect |
| 19. C2×#14583810 | C22 | semidirect |
| 20. M16×D173 | C22 | semidirect |
| 21. #19149598 | C22 | semidirect |
| 22. #19149596 | C22 | semidirect |
| 23. #19149595 | C22 | semidirect |
| 25. C2×M16×C173 | C22 | semidirect |
| 26. #101×C173 | C22 | semidirect |
| 27. #100×C173 | C22 | semidirect |
| 120. C173 | #2888 | semidirect |
| 126. #413 | D173 | semidirect |
| 143. C2×M16 | C2×D173 | semidirect |
| 145. #101 | C2×D173 | semidirect |
| 148. #100 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149725 | 2 |
| #26012257 | 2 |
| #26011475 | 2 |
| #26011474 | 2 |
| C2×#19149595 | 2 |
| #100×D173 | 2 |
| #413×C173 | 2 |
| #2888 | 173 |