Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
472 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 151 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. #23776541 | C2 | semidirect |
| 2. #23765713 | C2 | semidirect |
| 3. #23765712 | C2 | semidirect |
| 4. #23765707 | C2 | semidirect |
| 5. C2×#19098398 | C2 | semidirect |
| 6. #23765694 | C2 | semidirect |
| 7. C79×#3415 | C2 | semidirect |
| 10. #19098995 | C22 | semidirect |
| 11. C2×D1264 | C22 | semidirect |
| 12. #19098403 | C22 | semidirect |
| 13. #19098401 | C22 | semidirect |
| 14. #19098400 | C22 | semidirect |
| 15. #19098398 | C22 | semidirect |
| 16. #19098398 | C22 | semidirect |
| 17. #19098397 | C22 | semidirect |
| 18. C2×C79⋊C32 | C22 | semidirect |
| 21. #508×C79 | C22 | semidirect |
| 22. C2×D16×C79 | C22 | semidirect |
| 98. #3415 | D79 | semidirect |
| 104. C79 | #33982 | semidirect |
| 110. #508 | C2×D79 | semidirect |
| 112. C2×D16 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776541 | 2 |
| #23765713 | 2 |
| #23765712 | 2 |
| #23765707 | 2 |
| C2×#19098398 | 2 |
| #23765694 | 2 |
| C79×#3415 | 2 |
| #33982 | 79 |