Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×C4⋊Dic173 | C2 | semidirect |
| 2. #26011807 | C2 | direct (N × H) |
| 3. C2×#19149610 | C2 | semidirect |
| 4. C2×#19149600 | C2 | semidirect |
| 5. C2×C22⋊#13063436 | C2 | semidirect |
| 12. C2×C4⋊Dic173 | C22 | semidirect |
| 13. #19149610 | C22 | semidirect |
| 14. #19149600 | C22 | semidirect |
| 15. C22⋊#13063436 | C22 | semidirect |
| 91. C2×C173 | #481 | semidirect |
| 95. C173 | C2×#481 | semidirect |
| 187. C2 | #26011807 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic173 | 2 |
| #26011807 | 2 |
| C2×#19149610 | 2 |
| C2×#19149600 | 2 |
| C2×C22⋊#13063436 | 2 |
| C2×#121×C173 | 2 |
| C2×#481 | 173 |