Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19149701 | C2 | semidirect |
| 2. #26012002 | C2 | semidirect |
| 3. #26011732 | C2 | semidirect |
| 4. #26011727 | C2 | semidirect |
| 5. #26011720 | C2 | semidirect |
| 6. #26011529 | C2 | semidirect |
| 7. #26011488 | C2 | semidirect |
| 8. C23×C8×C173 | C2 | semidirect |
| 11. C2×Dic692 | C22 | semidirect |
| 12. C2×#14583815 | C22 | semidirect |
| 13. C2×D1384 | C22 | semidirect |
| 20. #19149613 | C22 | semidirect |
| 21. #19149611 | C22 | semidirect |
| 22. #19149604 | C22 | semidirect |
| 23. #19149601 | C22 | semidirect |
| 56. C2×C8×C173 | D4 | semidirect |
| 91. C22×C173 | #135 | semidirect |
| 106. C173 | #3050 | semidirect |
| 109. C23×C8 | D173 | semidirect |
| 157. C2×C8 | C22⋊D173 | semidirect |
| 200. C22 | #19149701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| #26012002 | 2 |
| #26011732 | 2 |
| #26011727 | 2 |
| #26011720 | 2 |
| #26011529 | 2 |
| #26011488 | 2 |
| C23×C8×C173 | 2 |
| #3050 | 173 |