Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23782210 | C2 | semidirect |
| 2. C2×D4×Dic163 | C2 | semidirect |
| 3. #23781979 | C2 | semidirect |
| 4. #23781976 | C2 | semidirect |
| 5. #23781943 | C2 | semidirect |
| 6. #23781858 | C2 | semidirect |
| 7. #23781799 | C2 | semidirect |
| 8. D8×Dic163 | C2 | semidirect |
| 9. #23781745 | C2 | semidirect |
| 10. #23781715 | C2 | semidirect |
| 11. #447×C163 | C2 | semidirect |
| 15. #19104734 | C22 | semidirect |
| 16. #19104731 | C22 | semidirect |
| 24. D4×Dic163 | C22 | semidirect |
| 25. #19104697 | C22 | semidirect |
| 30. #19104669 | C22 | semidirect |
| 31. #19104668 | C22 | semidirect |
| 32. Dic163⋊C8 | C22 | semidirect |
| 33. #19104657 | C22 | semidirect |
| 35. #19104656 | C22 | semidirect |
| 37. C8×Dic163 | C22 | semidirect |
| 96. C2×Dic163 | D8 | semidirect |
| 113. D4×C163 | #41 | semidirect |
| 149. C163 | #3100 | semidirect |
| 158. #447 | D163 | semidirect |
| 249. D4 | #14579698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782210 | 2 |
| C2×D4×Dic163 | 2 |
| #23781979 | 2 |
| #23781976 | 2 |
| #23781943 | 2 |
| #23781858 | 2 |
| #23781799 | 2 |
| D8×Dic163 | 2 |
| #23781745 | 2 |
| #23781715 | 2 |
| #447×C163 | 2 |
| #3100 | 163 |