Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
486 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23762062 | C2 | semidirect |
| 3. #23761544 | C2 | semidirect |
| 4. C79×#2126 | C2 | semidirect |
| 5. #19099399 | C4 | semidirect |
| 8. #19098740 | C4 | semidirect |
| 13. #19098547 | C4 | semidirect |
| 15. #19098307 | C22 | semidirect |
| 19. #353×C79 | C22 | semidirect |
| 175. #2126 | D79 | semidirect |
| 178. C79 | #13560 | semidirect |
| 191. #353 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772748 | 2 |
| #23762062 | 2 |
| #23761544 | 2 |
| C79×#2126 | 2 |
| #13560 | 79 |