Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
326 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23761571 | C2 | semidirect |
| 8. C2×#125×C79 | C4 | semidirect |
| 9. #491×C79 | C4 | semidirect |
| 13. C4×M16×C79 | C4 | semidirect |
| 97. C79 | #13596 | semidirect |
| 99. C2×#125 | Dic79 | semidirect |
| 100. #491 | Dic79 | semidirect |
| 105. C4×M16 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765065 | 2 |
| #23761571 | 2 |
| C79×#3142 | 2 |
| #13596 | 79 |