Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
560 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23763497 | C2 | semidirect |
| 4. #23761285 | C2 | semidirect |
| 8. #19098502 | C4 | semidirect |
| 9. #19098499 | C4 | semidirect |
| 10. #19098493 | C4 | semidirect |
| 12. #19098488 | C4 | semidirect |
| 189. C79 | #9011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766659 | 2 |
| #23763497 | 2 |
| C4×#14579076 | 2 |
| #23761285 | 2 |
| C79×#2973 | 2 |
| #9011 | 79 |