Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
340 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 97 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×C22⋊#13063436 | C2 | semidirect |
| 2. #26011351 | C2 | semidirect |
| 3. #26011225 | C2 | semidirect |
| 9. C22⋊#13063436 | C22 | semidirect |
| 10. #19149586 | C22 | semidirect |
| 12. C22×D4×C173 | C4 | semidirect |
| 16. #121×C173 | C4 | semidirect |
| 18. C2×C4⋊C4×C173 | C4 | semidirect |
| 109. C173 | #1519 | semidirect |
| 116. C22×D4 | Dic173 | semidirect |
| 121. #121 | Dic173 | semidirect |
| 124. C2×C4⋊C4 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#13063436 | 2 |
| #26011351 | 2 |
| #26011225 | 2 |
| C2×#121×C173 | 2 |
| #1519 | 173 |