Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
656 conjugacy classes of subgroups; only the 317 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 317 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 |
|---|---|---|
| 3. #26011390 | C2 | semidirect |
| 5. C4×C4⋊Dic173 | C2 | semidirect |
| 18. #117×C173 | C4 | semidirect |
| 39. C4⋊C4×C173 | C2×C4 | semidirect |
| 41. C42×C173 | C2×C4 | semidirect |
| 54. C2×C4×C173 | C4⋊C4 | semidirect |
| 80. C173 | #2296 | semidirect |
| 91. #117 | Dic173 | semidirect |
| 116. C4⋊C4 | C2×Dic173 | semidirect |
| 122. C42 | C2×Dic173 | semidirect |
| 135. C2×C4 | C4⋊Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149638 | 2 |
| C22×C4×Dic173 | 2 |
| #26011390 | 2 |
| #26011366 | 2 |
| C4×C4⋊Dic173 | 2 |
| C2×#117×C173 | 2 |
| #2296 | 173 |