Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23763200 | C2 | semidirect |
| 3. #23761523 | C2 | semidirect |
| 4. #23761521 | C2 | semidirect |
| 9. #19098353 | C4 | semidirect |
| 10. #19098350 | C4 | semidirect |
| 13. C23×C8×C79 | C4 | semidirect |
| 17. #424×C79 | C4 | semidirect |
| 19. #407×C79 | C4 | semidirect |
| 20. #405×C79 | C4 | semidirect |
| 154. C79 | #12623 | semidirect |
| 156. C23×C8 | Dic79 | semidirect |
| 160. #424 | Dic79 | semidirect |
| 164. #407 | Dic79 | semidirect |
| 166. #405 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765041 | 2 |
| #23763200 | 2 |
| #23761523 | 2 |
| #23761521 | 2 |
| C79×#2929 | 2 |
| #12623 | 79 |