Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 123 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×#19149702 | C2 | semidirect |
| 2. C2×#19149701 | C2 | semidirect |
| 3. #26012143 | C2 | semidirect |
| 4. #26011869 | C2 | semidirect |
| 5. #26011733 | C2 | semidirect |
| 6. #26011695 | C2 | semidirect |
| 7. #26011656 | C2 | semidirect |
| 8. #26011651 | C2 | semidirect |
| 9. #26011573 | C2 | semidirect |
| 10. C8×C22⋊D173 | C2 | semidirect |
| 11. #467×C173 | C2 | semidirect |
| 58. D1384 | D4 | semidirect |
| 129. Dic173 | #135 | semidirect |
| 136. C173 | #3283 | semidirect |
| 143. #467 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149702 | 2 |
| C2×#19149701 | 2 |
| #26012143 | 2 |
| #26011869 | 2 |
| #26011733 | 2 |
| #26011695 | 2 |
| #26011656 | 2 |
| #26011651 | 2 |
| #26011573 | 2 |
| C8×C22⋊D173 | 2 |
| #467×C173 | 2 |
| #3283 | 173 |