Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
538 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 538 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 |
|---|---|---|
| 8. #380×C79 | C4 | semidirect |
| 10. C4×C22⋊C4×C79 | C4 | semidirect |
| 101. C79 | #8750 | semidirect |
| 104. #380 | Dic79 | semidirect |
| 107. C4×C22⋊C4 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763474 | 2 |
| C79⋊#1304 | 2 |
| C79×#2312 | 2 |
| #8750 | 79 |