Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 29. #14579080 | Q8 | semidirect |
| 45. #101×C79 | Q8 | semidirect |
| 137. C79 | #13464 | semidirect |
| 173. #101 | Dic158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771393 | 2 |
| #23763615 | 2 |
| #23761527 | 2 |
| #23761526 | 2 |
| C79×#1857 | 2 |
| #13464 | 79 |