Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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×#19149622 | C2 | semidirect |
| 2. C2×D2768 | C2 | semidirect |
| 3. C2×#19149620 | C2 | semidirect |
| 4. #26011876 | C2 | semidirect |
| 5. #26011866 | C2 | semidirect |
| 6. #26011266 | C2 | semidirect |
| 7. C2×SD32×C173 | C2 | semidirect |
| 35. #14583801 | D4 | semidirect |
| 43. C16×C173 | D4 | semidirect |
| 78. C173 | #2250 | semidirect |
| 81. C2×SD32 | D173 | semidirect |
| 122. C16 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149622 | 2 |
| C2×D2768 | 2 |
| C2×#19149620 | 2 |
| #26011876 | 2 |
| #26011866 | 2 |
| #26011266 | 2 |
| C2×SD32×C173 | 2 |
| #2250 | 173 |