Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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. #23782137 | C2 | semidirect |
| 3. #23781778 | C2 | semidirect |
| 4. #23781777 | C2 | semidirect |
| 5. #23781776 | C2 | semidirect |
| 6. C4×#14579684 | C2 | semidirect |
| 7. #23781745 | C2 | semidirect |
| 8. #23781700 | C2 | semidirect |
| 9. #23781668 | C2 | semidirect |
| 10. #23781622 | C2 | semidirect |
| 11. #442×C163 | C2 | semidirect |
| 15. D8×D163 | C4 | semidirect |
| 18. C4×D652 | C22 | semidirect |
| 19. D4×Dic163 | C22 | semidirect |
| 20. #19104697 | C22 | semidirect |
| 27. #19104668 | C22 | semidirect |
| 28. #19104667 | C22 | semidirect |
| 29. #19104657 | C22 | semidirect |
| 30. #19104656 | C22 | semidirect |
| 31. #19104655 | C22 | semidirect |
| 32. #19104645 | C22 | semidirect |
| 33. C4×C163⋊C8 | C22 | semidirect |
| 34. C8×Dic163 | C22 | semidirect |
| 36. C4×D4×C163 | C22 | semidirect |
| 37. #106×C163 | C22 | semidirect |
| 38. #102×C163 | C22 | semidirect |
| 39. #97×C163 | C22 | semidirect |
| 44. D4×D163 | C2×C4 | semidirect |
| 49. D1304 | C2×C4 | semidirect |
| 50. #14579684 | C2×C4 | semidirect |
| 54. C8×D163 | C2×C4 | semidirect |
| 66. D8×C163 | C2×C4 | semidirect |
| 121. C163 | #2948 | semidirect |
| 128. #442 | D163 | semidirect |
| 146. C4×D4 | C2×D163 | semidirect |
| 153. #106 | C2×D163 | semidirect |
| 157. #102 | C2×D163 | semidirect |
| 159. #97 | C2×D163 | semidirect |
| 175. D8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D163 | 2 |
| #23782137 | 2 |
| #23781778 | 2 |
| #23781777 | 2 |
| #23781776 | 2 |
| C4×#14579684 | 2 |
| #23781745 | 2 |
| #23781700 | 2 |
| #23781668 | 2 |
| #23781622 | 2 |
| #442×C163 | 2 |
| #2948 | 163 |