Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. #23782431 | C2 | semidirect |
| 3. #23781788 | C2 | semidirect |
| 4. #23781783 | C2 | semidirect |
| 5. #23781714 | C2 | semidirect |
| 6. C2×#19104663 | C2 | semidirect |
| 7. C4×M16×C163 | C2 | semidirect |
| 9. #19104768 | C4 | semidirect |
| 10. #19104763 | C4 | semidirect |
| 13. #19104741 | C22 | semidirect |
| 16. #19104671 | C22 | semidirect |
| 17. #19104663 | C22 | semidirect |
| 18. #19104663 | C22 | semidirect |
| 22. #97×C163 | C22 | semidirect |
| 23. C4×C8×C163 | C22 | semidirect |
| 32. Dic652 | C2×C4 | semidirect |
| 33. #14579688 | C2×C4 | semidirect |
| 34. D1304 | C2×C4 | semidirect |
| 85. C163 | #2956 | semidirect |
| 93. C4×M16 | D163 | semidirect |
| 108. #97 | C2×D163 | semidirect |
| 109. C4×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782465 | 2 |
| #23782431 | 2 |
| #23781788 | 2 |
| #23781783 | 2 |
| #23781714 | 2 |
| C2×#19104663 | 2 |
| C4×M16×C163 | 2 |
| #2956 | 163 |