Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
380 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 9. #19098287 | C4 | semidirect |
| 10. C23×C8×C79 | C4 | semidirect |
| 13. C2×C22⋊C8×C79 | C4 | semidirect |
| 19. #14579076 | C8 | semidirect |
| 152. C79 | #7204 | semidirect |
| 153. C23×C8 | Dic79 | semidirect |
| 158. C2×C22⋊C8 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579076 | 2 |
| #23761721 | 2 |
| C79×#1869 | 2 |
| #7204 | 79 |