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. #23774146 | C2 | semidirect |
| 2. #23774116 | C2 | semidirect |
| 4. #23773771 | C2 | semidirect |
| 5. #23763071 | C2 | semidirect |
| 6. #23763052 | C2 | semidirect |
| 7. #23763037 | C2 | semidirect |
| 8. #23763005 | C2 | semidirect |
| 9. #23763002 | C2 | semidirect |
| 10. #23761704 | C2 | semidirect |
| 11. C79×#1715 | C2 | semidirect |
| 16. #19098968 | C22 | semidirect |
| 18. #19098943 | C22 | semidirect |
| 23. #19098915 | C22 | semidirect |
| 24. #19098913 | C22 | semidirect |
| 28. #19098909 | C22 | semidirect |
| 36. #19098285 | C22 | semidirect |
| 37. C8×C79⋊C8 | C22 | semidirect |
| 38. #498×C79 | C22 | semidirect |
| 40. #492×C79 | C22 | semidirect |
| 42. #322×C79 | C22 | semidirect |
| 195. #1715 | D79 | semidirect |
| 199. C79 | #19749 | semidirect |
| 205. #498 | C2×D79 | semidirect |
| 212. #492 | C2×D79 | semidirect |
| 229. #322 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774146 | 2 |
| #23774116 | 2 |
| #23773851 | 2 |
| #23773771 | 2 |
| #23763071 | 2 |
| #23763052 | 2 |
| #23763037 | 2 |
| #23763005 | 2 |
| #23763002 | 2 |
| #23761704 | 2 |
| C79×#1715 | 2 |
| #19749 | 79 |