Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #23782145 | C2 | semidirect |
| 3. #23781988 | C2 | semidirect |
| 4. #23781987 | C2 | semidirect |
| 5. #23781982 | C2 | semidirect |
| 6. #23781977 | C2 | semidirect |
| 7. #23781707 | C2 | semidirect |
| 8. #23781701 | C2 | semidirect |
| 9. C2×#19104656 | C2 | semidirect |
| 10. #23781633 | C2 | semidirect |
| 11. #418×C163 | C2 | semidirect |
| 23. #19104693 | C22 | semidirect |
| 25. C4⋊C4×D163 | C22 | semidirect |
| 26. #19104669 | C22 | semidirect |
| 27. #19104668 | C22 | semidirect |
| 28. #19104668 | C22 | semidirect |
| 29. #19104667 | C22 | semidirect |
| 30. #19104666 | C22 | semidirect |
| 31. #19104666 | C22 | semidirect |
| 34. (C2×D163)⋊C8 | C22 | semidirect |
| 35. (C2×D163)⋊C8 | C22 | semidirect |
| 134. C163 | #3096 | semidirect |
| 144. #418 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782232 | 2 |
| #23782145 | 2 |
| #23781988 | 2 |
| #23781987 | 2 |
| #23781982 | 2 |
| #23781977 | 2 |
| #23781707 | 2 |
| #23781701 | 2 |
| C2×#19104656 | 2 |
| #23781633 | 2 |
| #418×C163 | 2 |
| #3096 | 163 |