Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
760 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. #23765065 | C2 | semidirect |
| 2. #23763784 | C2 | semidirect |
| 4. #19099330 | C22 | semidirect |
| 6. #19098537 | C22 | semidirect |
| 10. #563×C79 | C4 | semidirect |
| 12. H(3,𝔽4)×C79 | C4 | semidirect |
| 130. C79 | #12772 | semidirect |
| 132. #563 | Dic79 | semidirect |
| 134. H(3,𝔽4) | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765065 | 2 |
| #23763784 | 2 |
| C79×#3529 | 2 |
| #12772 | 79 |