Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
342 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. C22×#11929608 | C4 | semidirect |
| 7. C2×C22⋊(C79⋊C8) | C4 | semidirect |
| 14. #323×C79 | C4 | semidirect |
| 151. C79 | #7320 | semidirect |
| 162. #323 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763698 | 2 |
| #23763388 | 2 |
| C79×#1466 | 2 |
| #7320 | 79 |