Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23782466 | C2 | semidirect |
| 2. #23782101 | C2 | semidirect |
| 3. #23782099 | C2 | semidirect |
| 4. #23782097 | C2 | semidirect |
| 5. #23782094 | C2 | semidirect |
| 6. D16×D163 | C2 | semidirect |
| 7. #23782081 | C2 | semidirect |
| 8. C2×D16×C163 | C2 | semidirect |
| 12. #19104757 | C22 | semidirect |
| 13. #19104754 | C22 | semidirect |
| 14. D8×D163 | C22 | semidirect |
| 16. Dic1304 | C22 | semidirect |
| 17. #19104680 | C22 | semidirect |
| 18. #19104679 | C22 | semidirect |
| 19. D2608 | C22 | semidirect |
| 20. #19104676 | C22 | semidirect |
| 21. #19104675 | C22 | semidirect |
| 22. #19104674 | C22 | semidirect |
| 23. C16×D163 | C22 | semidirect |
| 24. C2×D8×C163 | C22 | semidirect |
| 25. D16×C163 | C22 | semidirect |
| 26. D16×C163 | C22 | semidirect |
| 27. C2×C16×C163 | C22 | semidirect |
| 84. C163 | #3415 | semidirect |
| 92. C2×D16 | D163 | semidirect |
| 100. C2×D8 | C2×D163 | semidirect |
| 107. D16 | C2×D163 | semidirect |
| 108. D16 | C2×D163 | semidirect |
| 112. C2×C16 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782466 | 2 |
| #23782101 | 2 |
| #23782099 | 2 |
| #23782097 | 2 |
| #23782094 | 2 |
| D16×D163 | 2 |
| #23782081 | 2 |
| C2×D16×C163 | 2 |
| #3415 | 163 |