Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23772414 | C2 | semidirect |
| 3. #23761991 | C2 | semidirect |
| 4. #23761907 | C2 | semidirect |
| 5. #23761293 | C2 | semidirect |
| 6. #23761272 | C2 | semidirect |
| 7. C79×#1759 | C2 | semidirect |
| 10. #19098848 | C4 | semidirect |
| 11. #19098843 | C4 | semidirect |
| 12. #19098763 | C4 | semidirect |
| 13. #19098758 | C4 | semidirect |
| 205. #1759 | D79 | semidirect |
| 210. C79 | #9161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773551 | 2 |
| #23772414 | 2 |
| #23761991 | 2 |
| #23761907 | 2 |
| #23761293 | 2 |
| #23761272 | 2 |
| C79×#1759 | 2 |
| #9161 | 79 |