Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
408 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. C2×#19149738 | C2 | semidirect |
| 2. C2×#19149737 | C2 | semidirect |
| 3. #26012433 | C2 | semidirect |
| 4. C4×C22⋊#10621924 | C2 | semidirect |
| 15. C22×C22⋊D173 | C4 | semidirect |
| 22. C2×#14583805 | C4 | semidirect |
| 23. C2×#14583803 | C4 | semidirect |
| 24. C2×C22⋊C4×C173 | C4 | semidirect |
| 31. C22⋊#10621924 | D4 | semidirect |
| 133. Dic173 | #99 | semidirect |
| 143. C173 | #1964 | semidirect |
| 163. C2×C22⋊C4 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149738 | 2 |
| C2×#19149737 | 2 |
| #26012433 | 2 |
| C4×C22⋊#10621924 | 2 |
| C2×#19149652 | 2 |
| #1964 | 173 |