Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #23782372 | C2 | semidirect |
| 3. #23782012 | C2 | semidirect |
| 4. #23781984 | C2 | semidirect |
| 5. #23781956 | C2 | semidirect |
| 6. #23781894 | C2 | semidirect |
| 7. #23781866 | C2 | semidirect |
| 8. #23781818 | C2 | semidirect |
| 9. C4×#14579688 | C2 | semidirect |
| 10. C2×#19104657 | C2 | semidirect |
| 11. C8×D4×C163 | C2 | semidirect |
| 15. C2×#14579688 | C22 | semidirect |
| 16. #19104735 | C22 | semidirect |
| 19. #19104714 | C22 | semidirect |
| 24. C4×Dic326 | C22 | semidirect |
| 27. C2×C4⋊Dic163 | C22 | semidirect |
| 28. #19104667 | C22 | semidirect |
| 29. #19104667 | C22 | semidirect |
| 30. #19104660 | C22 | semidirect |
| 33. #19104657 | C22 | semidirect |
| 34. #19104657 | C22 | semidirect |
| 35. #19104657 | C22 | semidirect |
| 36. C22×C8×C163 | C22 | semidirect |
| 38. C4⋊C8×C163 | C22 | semidirect |
| 39. C22⋊C8×C163 | C22 | semidirect |
| 40. C4×C8×C163 | C22 | semidirect |
| 100. D4×C163 | SD16 | semidirect |
| 136. C163 | #3295 | semidirect |
| 147. C8×D4 | D163 | semidirect |
| 153. C22×C8 | C2×D163 | semidirect |
| 169. C4⋊C8 | C2×D163 | semidirect |
| 176. C22⋊C8 | C2×D163 | semidirect |
| 177. C4×C8 | C2×D163 | semidirect |
| 231. D4 | #14579688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782372 | 2 |
| D4×D652 | 2 |
| #23782012 | 2 |
| #23781984 | 2 |
| #23781956 | 2 |
| #23781894 | 2 |
| #23781866 | 2 |
| #23781818 | 2 |
| C4×#14579688 | 2 |
| C2×#19104657 | 2 |
| C8×D4×C163 | 2 |
| #3295 | 163 |