Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 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. #23782199 | C2 | semidirect |
| 2. C2×C4×D652 | C2 | semidirect |
| 3. #23781996 | C2 | semidirect |
| 4. #23781979 | C2 | semidirect |
| 5. #23781966 | C2 | semidirect |
| 6. #23781881 | C2 | semidirect |
| 7. #23781818 | C2 | semidirect |
| 9. #23781778 | C2 | semidirect |
| 10. #23781767 | C2 | semidirect |
| 11. #432×C163 | C2 | semidirect |
| 17. #19104727 | C22 | semidirect |
| 18. #19104723 | C22 | semidirect |
| 22. C4×Dic326 | C22 | semidirect |
| 27. C4×D652 | C22 | semidirect |
| 32. #19104669 | C22 | semidirect |
| 33. #19104667 | C22 | semidirect |
| 34. #19104660 | C22 | semidirect |
| 37. #19104657 | C22 | semidirect |
| 39. C4⋊C8×C163 | C22 | semidirect |
| 42. #97×C163 | C22 | semidirect |
| 140. C163 | #3114 | semidirect |
| 152. #432 | D163 | semidirect |
| 176. C4⋊C8 | C2×D163 | semidirect |
| 183. #97 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782199 | 2 |
| C2×C4×D652 | 2 |
| #23781996 | 2 |
| #23781979 | 2 |
| #23781966 | 2 |
| #23781881 | 2 |
| #23781818 | 2 |
| #23781801 | 2 |
| #23781778 | 2 |
| #23781767 | 2 |
| #432×C163 | 2 |
| #3114 | 163 |