Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
388 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 2. #26012450 | C2 | semidirect |
| 3. C4×C4⋊#10621924 | C2 | semidirect |
| 4. #26012364 | C2 | semidirect |
| 9. #19149741 | C4 | semidirect |
| 15. C4×D692 | C4 | semidirect |
| 16. D4×Dic173 | C4 | semidirect |
| 17. #19149641 | C4 | semidirect |
| 23. C4×D4×C173 | C4 | semidirect |
| 26. D173⋊C8 | C2×C4 | semidirect |
| 29. C4⋊#10621924 | C2×C4 | semidirect |
| 68. D692 | C42 | semidirect |
| 85. D4×C173 | C42 | semidirect |
| 121. C173 | #1762 | semidirect |
| 136. C4×D4 | #10621924 | semidirect |
| 190. D4 | C4×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149741 | 2 |
| #26012450 | 2 |
| C4×C4⋊#10621924 | 2 |
| #26012364 | 2 |
| C4×D4×D173 | 2 |
| #1762 | 173 |