Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
504 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 111 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×#19098345 | C2 | semidirect |
| 3. #23761337 | C2 | semidirect |
| 4. C2×#349×C79 | C2 | semidirect |
| 15. #19098345 | C22 | semidirect |
| 19. #349×C79 | C22 | semidirect |
| 190. C2×#349 | D79 | semidirect |
| 192. C79 | #11438 | semidirect |
| 207. #349 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771844 | 2 |
| C2×#19098345 | 2 |
| #23761337 | 2 |
| C2×#349×C79 | 2 |
| #11438 | 79 |