Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
880 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. C2×#19149594 | C2 | semidirect |
| 3. C2×#19149593 | C2 | semidirect |
| 4. #26011346 | C2 | semidirect |
| 5. C2×#99×C173 | C2 | semidirect |
| 6. C24×D173 | C4 | semidirect |
| 8. C22×D692 | C4 | semidirect |
| 9. C22×C22⋊D173 | C4 | semidirect |
| 15. C22×C4×D173 | C4 | semidirect |
| 16. C2×C22⋊Dic173 | C22 | semidirect |
| 21. C2×C22⋊C4×C173 | C22 | semidirect |
| 88. C22×D173 | C22⋊C4 | semidirect |
| 97. C2×Dic173 | C22⋊C4 | semidirect |
| 103. C23×C173 | C22⋊C4 | semidirect |
| 115. C2×C4×C173 | C22⋊C4 | semidirect |
| 145. C2×D173 | #99 | semidirect |
| 160. C173 | #1781 | semidirect |
| 165. C2×#99 | D173 | semidirect |
| 180. C2×C22⋊C4 | C2×D173 | semidirect |
| 254. C23 | #14583803 | semidirect |
| 276. C2×C4 | #14583803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D173 | 2 |
| C2×#19149594 | 2 |
| C2×#19149593 | 2 |
| #26011346 | 2 |
| C2×#99×C173 | 2 |
| #1781 | 173 |