Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1014 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1014 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23763312 | C2 | semidirect |
| 3. #23761954 | C2 | semidirect |
| 4. C79×#1782 | C2 | semidirect |
| 5. C2×#14579206 | C4 | semidirect |
| 8. #19099137 | C4 | semidirect |
| 12. #19099038 | C4 | semidirect |
| 14. C2×C22⋊(C79⋊C8) | C22 | semidirect |
| 19. #381×C79 | C22 | semidirect |
| 164. #1782 | D79 | semidirect |
| 167. C79 | #8462 | semidirect |
| 180. #381 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777044 | 2 |
| #23763312 | 2 |
| #23761954 | 2 |
| C79×#1782 | 2 |
| #8462 | 79 |