Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
992 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 992 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 |
|---|---|---|
| 1. #23774411 | C2 | semidirect |
| 2. #23773745 | C2 | semidirect |
| 3. #23762706 | C2 | semidirect |
| 4. #23762035 | C2 | semidirect |
| 5. #23762011 | C2 | semidirect |
| 7. #19099120 | C22 | semidirect |
| 8. #19098958 | C22 | semidirect |
| 11. #19098922 | C22 | semidirect |
| 12. #19098922 | C22 | semidirect |
| 16. #19098620 | C22 | semidirect |
| 18. C2×#14579072 | C22 | semidirect |
| 19. #19098303 | C22 | semidirect |
| 20. #19098303 | C22 | semidirect |
| 177. C79 | #19056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774411 | 2 |
| #23773745 | 2 |
| #23762706 | 2 |
| #23762035 | 2 |
| #23762011 | 2 |
| C79×#3549 | 2 |
| #19056 | 79 |