Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149705 | C2 | semidirect |
| 2. C2×#19149701 | C2 | semidirect |
| 3. #26012058 | C2 | semidirect |
| 4. #26011879 | C2 | semidirect |
| 5. #26011874 | C2 | semidirect |
| 6. #26011866 | C2 | semidirect |
| 7. #26011446 | C2 | semidirect |
| 8. C22×D8×C173 | C2 | semidirect |
| 12. C2×Dic692 | C22 | semidirect |
| 13. C2×#14583815 | C22 | semidirect |
| 14. C2×#14583814 | C22 | semidirect |
| 15. C2×D1384 | C22 | semidirect |
| 16. C2×#14583811 | C22 | semidirect |
| 18. #19149675 | C22 | semidirect |
| 19. #19149666 | C22 | semidirect |
| 23. #19149589 | C22 | semidirect |
| 24. C8×Dic173 | C22 | semidirect |
| 42. #14583810 | D4 | semidirect |
| 56. C2×C8×C173 | D4 | semidirect |
| 101. C173 | #3155 | semidirect |
| 105. C22×D8 | D173 | semidirect |
| 154. C2×C8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149705 | 2 |
| C2×#19149701 | 2 |
| #26012058 | 2 |
| #26011879 | 2 |
| #26011874 | 2 |
| #26011866 | 2 |
| #26011446 | 2 |
| C22×D8×C173 | 2 |
| #3155 | 173 |