Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
488 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 146 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. #26012361 | C2 | direct (N × H) |
| 8. C2×#14583836 | C4 | semidirect |
| 13. C2×C4×#10621924 | C4 | semidirect |
| 18. #19149637 | C4 | semidirect |
| 20. C2×C4⋊Dic173 | C4 | semidirect |
| 23. C2×C4⋊C4×C173 | C4 | semidirect |
| 30. #14583836 | C2×C4 | semidirect |
| 35. C4×#10621924 | C2×C4 | semidirect |
| 48. C4⋊Dic173 | C2×C4 | semidirect |
| 56. C4⋊C4×C173 | C2×C4 | semidirect |
| 113. C2×C173 | #339 | semidirect |
| 120. C173 | C2×#339 | semidirect |
| 138. C2×C4⋊C4 | #10621924 | semidirect |
| 170. C4⋊C4 | C2×#10621924 | semidirect |
| 237. C2 | #26012361 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583836 | 2 |
| C22×C4×#10621924 | 2 |
| #26012361 | 2 |
| C2×#19149637 | 2 |
| C2×#339 | 173 |