Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 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. #23763438 | C2 | semidirect |
| 4. #23761306 | C2 | semidirect |
| 5. C79×#1807 | C2 | semidirect |
| 6. C2×#14579167 | C4 | semidirect |
| 13. #19098589 | C4 | semidirect |
| 14. #19098529 | C4 | semidirect |
| 17. #19098518 | C4 | semidirect |
| 187. #1807 | D79 | semidirect |
| 190. C79 | #8629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772094 | 2 |
| #23763438 | 2 |
| #23761941 | 2 |
| #23761306 | 2 |
| C79×#1807 | 2 |
| #8629 | 79 |