Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
656 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 285 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. #26011389 | C2 | semidirect |
| 5. C4×#14583805 | C2 | semidirect |
| 8. #19149638 | C4 | semidirect |
| 25. C4⋊Dic173 | C2×C4 | semidirect |
| 30. C4×Dic173 | C2×C4 | semidirect |
| 54. C2×C4×C173 | C4⋊C4 | semidirect |
| 80. C173 | #2296 | semidirect |
| 135. C2×C4 | #14583805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149638 | 2 |
| #26011389 | 2 |
| #26011364 | 2 |
| C4×#14583805 | 2 |
| C22×C42×C173 | 2 |
| #2296 | 173 |