Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
448 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 138 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. #26012364 | C2 | semidirect |
| 7. D173⋊M16 | C4 | semidirect |
| 11. #19149758 | C4 | semidirect |
| 17. C2×C4⋊Dic173 | C4 | semidirect |
| 21. C4⋊C4×D173 | C4 | semidirect |
| 23. C2×C4⋊C4×C173 | C4 | semidirect |
| 28. D173⋊C8 | C2×C4 | semidirect |
| 31. C4⋊#10621924 | C2×C4 | semidirect |
| 120. C173 | #1736 | semidirect |
| 142. C2×C4⋊C4 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D173⋊M16 | 2 |
| C2×#19149758 | 2 |
| #26012364 | 2 |
| C2×C4⋊C4×D173 | 2 |
| #1736 | 173 |