Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 470 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. C2×#19098362 | C2 | semidirect |
| 3. #23761555 | C2 | semidirect |
| 4. C79×#1558 | C2 | semidirect |
| 15. #19098362 | C22 | semidirect |
| 19. #333×C79 | C22 | semidirect |
| 170. #1558 | D79 | semidirect |
| 172. C79 | #13573 | semidirect |
| 187. #333 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098745 | 2 |
| C2×#19098362 | 2 |
| #23761555 | 2 |
| C79×#1558 | 2 |
| #13573 | 79 |