Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 484 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×#19149701 | C2 | semidirect |
| 2. #26012069 | C2 | semidirect |
| 3. #26011737 | C2 | semidirect |
| 4. #26011732 | C2 | semidirect |
| 5. #26011727 | C2 | semidirect |
| 6. C2×#19149613 | C2 | semidirect |
| 7. #26011493 | C2 | semidirect |
| 8. C2×#131×C173 | C2 | semidirect |
| 56. C2×C8×C173 | D4 | semidirect |
| 108. C173 | #3061 | semidirect |
| 111. C2×#131 | D173 | semidirect |
| 160. 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×#19149701 | 2 |
| #26012069 | 2 |
| #26011737 | 2 |
| #26011732 | 2 |
| #26011727 | 2 |
| C2×#19149613 | 2 |
| #26011493 | 2 |
| C2×#131×C173 | 2 |
| #3061 | 173 |