Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
814 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 814 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. C79⋊#1304 | C2 | semidirect |
| 7. C22×C22⋊C4×C79 | C4 | semidirect |
| 9. #381×C79 | C4 | semidirect |
| 105. C79 | #8747 | semidirect |
| 107. C22×C22⋊C4 | Dic79 | semidirect |
| 110. #381 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763315 | 2 |
| C79⋊#1304 | 2 |
| C79×#2308 | 2 |
| #8747 | 79 |