Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
626 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23763388 | C2 | semidirect |
| 3. #23761422 | C2 | semidirect |
| 4. #23761398 | C2 | semidirect |
| 5. C79×#1466 | C2 | semidirect |
| 6. C22×#11929624 | C4 | semidirect |
| 9. #19098483 | C4 | semidirect |
| 10. #19098480 | C4 | semidirect |
| 17. C4×C22⋊Dic79 | C4 | semidirect |
| 221. #1466 | D79 | semidirect |
| 224. C79 | #11820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766615 | 2 |
| #23763388 | 2 |
| #23761422 | 2 |
| #23761398 | 2 |
| C79×#1466 | 2 |
| #11820 | 79 |