Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782480 | C2 | semidirect |
| 2. #23782475 | C2 | semidirect |
| 3. #23782060 | C2 | semidirect |
| 4. #23781939 | C2 | semidirect |
| 5. #23781926 | C2 | semidirect |
| 6. #23781849 | C2 | semidirect |
| 7. #23781842 | C2 | semidirect |
| 8. #23781784 | C2 | semidirect |
| 9. #454×C163 | C2 | semidirect |
| 16. #19104765 | C22 | semidirect |
| 23. C2×#14579689 | C22 | semidirect |
| 27. #19104742 | C22 | semidirect |
| 28. #19104735 | C22 | semidirect |
| 29. #19104670 | C22 | semidirect |
| 31. #19104653 | C22 | semidirect |
| 33. #19104646 | C22 | semidirect |
| 34. 2−1+4×C163 | C22 | semidirect |
| 37. #104×C163 | C22 | semidirect |
| 38. #101×C163 | C22 | semidirect |
| 129. C163 | #3289 | semidirect |
| 138. #454 | D163 | semidirect |
| 141. 2−1+4 | C2×D163 | semidirect |
| 164. #104 | C2×D163 | semidirect |
| 166. #101 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782480 | 2 |
| #23782475 | 2 |
| #23782060 | 2 |
| #23781939 | 2 |
| #23781926 | 2 |
| #23781849 | 2 |
| #23781842 | 2 |
| #23781784 | 2 |
| #454×C163 | 2 |
| #3289 | 163 |