Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. #23765608 | C2 | semidirect |
| 3. #23765591 | C2 | semidirect |
| 4. #23765186 | C2 | semidirect |
| 5. #23765110 | C2 | semidirect |
| 6. #23765011 | C2 | semidirect |
| 7. C2×#427×C79 | C2 | semidirect |
| 16. #19098390 | C22 | semidirect |
| 17. #19098388 | C22 | semidirect |
| 18. #19098366 | C22 | semidirect |
| 19. #19098363 | C22 | semidirect |
| 145. C2×#427 | D79 | semidirect |
| 151. C79 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772981 | 2 |
| #23765608 | 2 |
| #23765591 | 2 |
| #23765186 | 2 |
| #23765110 | 2 |
| #23765011 | 2 |
| C2×#427×C79 | 2 |
| #33647 | 79 |