Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
510 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 143 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. #23763176 | C2 | semidirect |
| 3. #23761287 | C2 | semidirect |
| 4. #23761285 | C2 | semidirect |
| 10. #19098300 | C4 | semidirect |
| 11. #19098297 | C4 | semidirect |
| 12. C2×#131×C79 | C4 | semidirect |
| 17. #424×C79 | C4 | semidirect |
| 18. #408×C79 | C4 | semidirect |
| 20. #405×C79 | C4 | semidirect |
| 149. C79 | #8239 | semidirect |
| 150. C2×#131 | Dic79 | semidirect |
| 155. #424 | Dic79 | semidirect |
| 156. #408 | Dic79 | semidirect |
| 159. #405 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763176 | 2 |
| #23761891 | 2 |
| #23761287 | 2 |
| #23761285 | 2 |
| C79×#2929 | 2 |
| #8239 | 79 |