Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
616 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 616 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 |
|---|---|---|
| 2. #23762110 | C2 | semidirect |
| 5. #23761950 | C2 | semidirect |
| 6. #23761872 | C2 | semidirect |
| 7. C79×#1515 | C2 | semidirect |
| 9. Q8×Dic158 | C4 | semidirect |
| 10. #19099292 | C4 | semidirect |
| 13. #19099286 | C4 | semidirect |
| 15. #19099273 | C4 | semidirect |
| 256. #1515 | D79 | semidirect |
| 258. C79 | #8501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777888 | 2 |
| #23762110 | 2 |
| #23762029 | 2 |
| #23761975 | 2 |
| #23761950 | 2 |
| #23761872 | 2 |
| C79×#1515 | 2 |
| #8501 | 79 |