Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
770 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23771845 | C2 | semidirect |
| 3. #23761928 | C2 | semidirect |
| 4. #23761252 | C2 | semidirect |
| 5. C79×#1782 | C2 | semidirect |
| 7. C2×#14579157 | C4 | semidirect |
| 8. C2×#14579150 | C4 | semidirect |
| 15. #19098470 | C4 | semidirect |
| 16. #19098466 | C4 | semidirect |
| 49. C22⋊(C79⋊C8) | D4 | semidirect |
| 249. #1782 | D79 | semidirect |
| 252. C79 | #9445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771845 | 2 |
| #23767015 | 2 |
| #23761928 | 2 |
| #23761252 | 2 |
| C79×#1782 | 2 |
| #9445 | 79 |