Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
764 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 202 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×#14583835 | C2 | semidirect |
| 2. #26012464 | C2 | semidirect |
| 3. #26012463 | C2 | semidirect |
| 4. #26012461 | C2 | semidirect |
| 8. C2×#14583835 | C22 | semidirect |
| 9. C22×#13063443 | C22 | semidirect |
| 10. #19149736 | C22 | semidirect |
| 11. C22⋊#13063443 | C22 | semidirect |
| 107. C173 | #2879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583835 | 2 |
| #26012464 | 2 |
| #26012463 | 2 |
| #26012461 | 2 |
| C22×#14583825 | 2 |
| #2879 | 173 |