Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
292 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 91 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×C79⋊C16 | C4 | semidirect |
| 13. #341×C79 | C4 | semidirect |
| 113. C79 | #7232 | semidirect |
| 122. #341 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C79⋊C16) | 2 |
| #23763425 | 2 |
| C79×#1810 | 2 |
| #7232 | 79 |