Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
822 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 1. #23774143 | C2 | semidirect |
| 2. #23774117 | C2 | semidirect |
| 4. #23773771 | C2 | semidirect |
| 5. #23763072 | C2 | semidirect |
| 6. #23763050 | C2 | semidirect |
| 7. #23763036 | C2 | semidirect |
| 8. #23763026 | C2 | semidirect |
| 9. #23763001 | C2 | semidirect |
| 10. #23761702 | C2 | semidirect |
| 11. C79×#1709 | C2 | semidirect |
| 16. #19098966 | C22 | semidirect |
| 17. #19098961 | C22 | semidirect |
| 22. #19098935 | C22 | semidirect |
| 24. #19098914 | C22 | semidirect |
| 25. #19098913 | C22 | semidirect |
| 36. #19098284 | C22 | semidirect |
| 37. #19098284 | C22 | semidirect |
| 38. #494×C79 | C22 | semidirect |
| 41. #486×C79 | C22 | semidirect |
| 42. C82×C79 | C22 | semidirect |
| 196. #1709 | D79 | semidirect |
| 199. C79 | #19749 | semidirect |
| 207. #494 | C2×D79 | semidirect |
| 220. #486 | C2×D79 | semidirect |
| 230. C82 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774143 | 2 |
| #23774117 | 2 |
| #23773851 | 2 |
| #23773771 | 2 |
| #23763072 | 2 |
| #23763050 | 2 |
| #23763036 | 2 |
| #23763026 | 2 |
| #23763001 | 2 |
| #23761702 | 2 |
| C79×#1709 | 2 |
| #19749 | 79 |