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. #23774121 | C2 | semidirect |
| 4. #23773771 | C2 | semidirect |
| 5. #23763069 | C2 | semidirect |
| 6. #23763054 | C2 | semidirect |
| 7. #23763040 | C2 | semidirect |
| 8. #23763029 | C2 | semidirect |
| 9. #23763006 | C2 | semidirect |
| 10. #23761702 | C2 | semidirect |
| 11. C79×#1708 | C2 | semidirect |
| 16. #19098966 | C22 | semidirect |
| 18. #19098943 | C22 | semidirect |
| 22. #19098937 | C22 | semidirect |
| 24. #19098915 | C22 | semidirect |
| 27. #19098910 | C22 | semidirect |
| 36. #19098284 | C22 | semidirect |
| 37. #19098284 | C22 | semidirect |
| 38. #498×C79 | C22 | semidirect |
| 40. #487×C79 | C22 | semidirect |
| 42. C82×C79 | C22 | semidirect |
| 197. #1708 | D79 | semidirect |
| 199. C79 | #19749 | semidirect |
| 205. #498 | C2×D79 | semidirect |
| 215. #487 | 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 |
|---|---|
| #23774146 | 2 |
| #23774121 | 2 |
| #23773847 | 2 |
| #23773771 | 2 |
| #23763069 | 2 |
| #23763054 | 2 |
| #23763040 | 2 |
| #23763029 | 2 |
| #23763006 | 2 |
| #23761702 | 2 |
| C79×#1708 | 2 |
| #19749 | 79 |