Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#14583815 | C2 | semidirect |
| 3. #26012062 | C2 | semidirect |
| 4. #26011965 | C2 | semidirect |
| 5. #26011705 | C2 | semidirect |
| 6. #26011695 | C2 | semidirect |
| 7. #26011517 | C2 | semidirect |
| 8. #26011499 | C2 | semidirect |
| 9. #416×C173 | C2 | semidirect |
| 18. #19149677 | C22 | semidirect |
| 19. #19149666 | C22 | semidirect |
| 26. #19149608 | C22 | semidirect |
| 27. #19149602 | C22 | semidirect |
| 31. #103×C173 | C22 | semidirect |
| 32. #102×C173 | C22 | semidirect |
| 116. C173 | #3042 | semidirect |
| 126. #416 | D173 | semidirect |
| 148. #103 | C2×D173 | semidirect |
| 149. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149704 | 2 |
| C22×#14583815 | 2 |
| #26012062 | 2 |
| #26011965 | 2 |
| #26011705 | 2 |
| #26011695 | 2 |
| #26011517 | 2 |
| #26011499 | 2 |
| #416×C173 | 2 |
| #3042 | 173 |