Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
564 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 373 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. #26011447 | C2 | semidirect |
| 3. C4×#14583810 | C2 | semidirect |
| 5. C2×#14583810 | C4 | semidirect |
| 9. #19149590 | C22 | semidirect |
| 10. C4×#13063436 | C22 | semidirect |
| 18. #14583810 | C2×C4 | semidirect |
| 19. C2×#13063436 | C2×C4 | semidirect |
| 61. C173 | #2873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583810 | 2 |
| #26011447 | 2 |
| C4×#14583810 | 2 |
| C2×#117×C173 | 2 |
| #2873 | 173 |