Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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. #117×D163 | C2 | semidirect |
| 3. #23781988 | C2 | semidirect |
| 4. #23781987 | C2 | semidirect |
| 5. #23781982 | C2 | semidirect |
| 6. #23781977 | C2 | semidirect |
| 7. #23781708 | C2 | semidirect |
| 8. #23781707 | C2 | semidirect |
| 9. #23781670 | C2 | semidirect |
| 10. #23781628 | C2 | semidirect |
| 11. #418×C163 | C2 | semidirect |
| 20. #19104693 | C22 | semidirect |
| 21. #19104693 | C22 | semidirect |
| 25. C4⋊C4×D163 | C22 | semidirect |
| 26. C4⋊C4×D163 | C22 | semidirect |
| 30. #19104669 | C22 | semidirect |
| 31. #19104668 | C22 | semidirect |
| 32. #19104667 | C22 | semidirect |
| 33. #19104666 | C22 | semidirect |
| 34. #19104656 | C22 | semidirect |
| 35. #19104656 | C22 | semidirect |
| 36. (C2×D163)⋊C8 | C22 | semidirect |
| 37. (C2×D163)⋊C8 | C22 | semidirect |
| 41. #102×C163 | C22 | semidirect |
| 42. #102×C163 | C22 | semidirect |
| 155. C163 | #3094 | semidirect |
| 166. #418 | D163 | semidirect |
| 195. #102 | C2×D163 | semidirect |
| 196. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104706 | 2 |
| #117×D163 | 2 |
| #23781988 | 2 |
| #23781987 | 2 |
| #23781982 | 2 |
| #23781977 | 2 |
| #23781708 | 2 |
| #23781707 | 2 |
| #23781670 | 2 |
| #23781628 | 2 |
| #418×C163 | 2 |
| #3094 | 163 |