Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23782501 | C2 | semidirect |
| 2. C2×#19104761 | C2 | semidirect |
| 3. #23781837 | C2 | semidirect |
| 4. #23781832 | C2 | semidirect |
| 5. #23781683 | C2 | semidirect |
| 6. #23781649 | C2 | semidirect |
| 7. #535×C163 | C2 | semidirect |
| 8. #19104783 | C22 | semidirect |
| 12. #19104780 | C22 | semidirect |
| 17. #19104761 | C22 | semidirect |
| 20. C2×#14579683 | C22 | semidirect |
| 21. #19104663 | C22 | semidirect |
| 22. #19104654 | C22 | semidirect |
| 23. #19104652 | C22 | semidirect |
| 25. C22×D4×C163 | C22 | semidirect |
| 26. #127×C163 | C22 | semidirect |
| 27. #124×C163 | C22 | semidirect |
| 30. #117×C163 | C22 | semidirect |
| 37. #14579699 | D4 | semidirect |
| 42. C2×Dic326 | D4 | semidirect |
| 45. C2×D652 | D4 | semidirect |
| 134. C163 | #3021 | semidirect |
| 138. #535 | D163 | semidirect |
| 152. C22×D4 | C2×D163 | semidirect |
| 158. #127 | C2×D163 | semidirect |
| 159. #124 | C2×D163 | semidirect |
| 162. #117 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782501 | 2 |
| C2×#19104761 | 2 |
| #23781837 | 2 |
| #23781832 | 2 |
| #23781683 | 2 |
| #23781649 | 2 |
| #535×C163 | 2 |
| #3021 | 163 |