Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
786 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. C79⋊#1304 | C2 | semidirect |
| 5. C2×#14579120 | C4 | semidirect |
| 9. #19098419 | C4 | semidirect |
| 138. C79 | #8748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765982 | 2 |
| #23763315 | 2 |
| C79⋊#1304 | 2 |
| C79×#1781 | 2 |
| #8748 | 79 |