Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 143 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×#19149710 | C2 | semidirect |
| 3. C2×Q8×Dic173 | C2 | semidirect |
| 4. #26011715 | C2 | semidirect |
| 5. #26011711 | C2 | semidirect |
| 6. #26011699 | C2 | semidirect |
| 7. #26011689 | C2 | semidirect |
| 8. #26011514 | C2 | semidirect |
| 9. #26011493 | C2 | semidirect |
| 10. #26011492 | C2 | semidirect |
| 11. C2×#137×C173 | C2 | semidirect |
| 80. C2×Q8×C173 | D4 | semidirect |
| 150. Dic173 | #137 | semidirect |
| 157. C173 | #3037 | semidirect |
| 160. C2×#137 | D173 | semidirect |
| 210. C2×Q8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149710 | 2 |
| #26012037 | 2 |
| C2×Q8×Dic173 | 2 |
| #26011715 | 2 |
| #26011711 | 2 |
| #26011699 | 2 |
| #26011689 | 2 |
| #26011514 | 2 |
| #26011493 | 2 |
| #26011492 | 2 |
| C2×#137×C173 | 2 |
| #3037 | 173 |