Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#14583816 | C2 | semidirect |
| 2. C22×#14583814 | C2 | semidirect |
| 3. C2×#19149658 | C2 | semidirect |
| 4. #26011653 | C2 | direct (N × H) |
| 5. C2×#19149603 | C2 | semidirect |
| 6. C2×#19149600 | C2 | semidirect |
| 7. C2×C22⋊#13063436 | C2 | semidirect |
| 11. C2×#14583816 | C22 | semidirect |
| 13. C2×#14583814 | C22 | semidirect |
| 17. #19149658 | C22 | semidirect |
| 21. #19149603 | C22 | semidirect |
| 22. #19149600 | C22 | semidirect |
| 23. C22⋊#13063436 | C22 | semidirect |
| 131. C2×C173 | #452 | semidirect |
| 135. C173 | C2×#452 | semidirect |
| 267. C2 | #26011653 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583816 | 2 |
| C22×#14583814 | 2 |
| C2×#19149658 | 2 |
| #26011653 | 2 |
| C2×#19149603 | 2 |
| C2×#19149600 | 2 |
| C2×C22⋊#13063436 | 2 |
| C22×#41×C173 | 2 |
| C2×#452 | 173 |