Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19149698 | C2 | semidirect |
| 2. #26012140 | C2 | semidirect |
| 3. #26011869 | C2 | semidirect |
| 4. #26011732 | C2 | semidirect |
| 5. #26011729 | C2 | semidirect |
| 6. #26011694 | C2 | semidirect |
| 7. #26011653 | C2 | semidirect |
| 8. #26011650 | C2 | semidirect |
| 9. D8×Dic173 | C2 | semidirect |
| 10. C8×C22⋊D173 | C2 | semidirect |
| 11. C2×#135×C173 | C2 | semidirect |
| 76. D8×C173 | D4 | semidirect |
| 129. Dic173 | #135 | semidirect |
| 136. C173 | #3283 | semidirect |
| 139. C2×#135 | D173 | semidirect |
| 198. D8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149698 | 2 |
| #26012140 | 2 |
| #26011869 | 2 |
| #26011732 | 2 |
| #26011729 | 2 |
| #26011694 | 2 |
| #26011653 | 2 |
| #26011650 | 2 |
| D8×Dic173 | 2 |
| C8×C22⋊D173 | 2 |
| C2×#135×C173 | 2 |
| #3283 | 173 |