Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 3. #23763620 | C2 | semidirect |
| 4. #23761528 | C2 | semidirect |
| 13. #19098362 | C4 | semidirect |
| 14. #19098360 | C4 | semidirect |
| 142. C79 | #12975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772467 | 2 |
| #23765085 | 2 |
| #23763620 | 2 |
| #23761528 | 2 |
| C79×#1884 | 2 |
| #12975 | 79 |