Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782376 | C2 | semidirect |
| 3. #23782013 | C2 | semidirect |
| 4. #23781985 | C2 | semidirect |
| 5. #23781895 | C2 | semidirect |
| 6. #23781866 | C2 | semidirect |
| 7. #23781817 | C2 | semidirect |
| 8. C4×#14579687 | C2 | semidirect |
| 9. #23781730 | C2 | semidirect |
| 10. #102×D163 | C2 | semidirect |
| 11. #476×C163 | C2 | semidirect |
| 14. C2×#14579688 | C22 | semidirect |
| 16. C2×C8×D163 | C22 | semidirect |
| 19. #19104715 | C22 | semidirect |
| 24. C4×Dic326 | C22 | semidirect |
| 27. C4⋊C4×D163 | C22 | semidirect |
| 28. #19104666 | C22 | semidirect |
| 29. #19104658 | C22 | semidirect |
| 30. #19104657 | C22 | semidirect |
| 32. #19104655 | C22 | semidirect |
| 33. #19104655 | C22 | semidirect |
| 34. (C2×D163)⋊C8 | C22 | semidirect |
| 35. C4×C163⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C163 | C22 | semidirect |
| 38. #106×C163 | C22 | semidirect |
| 39. C4⋊C8×C163 | C22 | semidirect |
| 89. D652 | SD16 | semidirect |
| 136. C163 | #3295 | semidirect |
| 142. #476 | D163 | semidirect |
| 154. C4⋊Q8 | C2×D163 | semidirect |
| 168. #106 | C2×D163 | semidirect |
| 169. C4⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782376 | 2 |
| D4×D652 | 2 |
| #23782013 | 2 |
| #23781985 | 2 |
| #23781895 | 2 |
| #23781866 | 2 |
| #23781817 | 2 |
| C4×#14579687 | 2 |
| #23781730 | 2 |
| #102×D163 | 2 |
| #476×C163 | 2 |
| #3295 | 163 |