Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1002 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 139 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. #23763318 | C2 | semidirect |
| 2. #23763312 | C2 | semidirect |
| 3. #23761956 | C2 | semidirect |
| 11. C2×2−1+4×C79 | C4 | semidirect |
| 16. #535×C79 | C4 | semidirect |
| 19. #519×C79 | C4 | semidirect |
| 165. C79 | #8464 | semidirect |
| 166. C2×2−1+4 | Dic79 | semidirect |
| 171. #535 | Dic79 | semidirect |
| 174. #519 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763318 | 2 |
| #23763312 | 2 |
| #23761956 | 2 |
| C79×#3487 | 2 |
| #8464 | 79 |