Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23782296 | C2 | semidirect |
| 3. #23781968 | C2 | semidirect |
| 4. #23781964 | C2 | semidirect |
| 5. #23781954 | C2 | semidirect |
| 6. #23781944 | C2 | semidirect |
| 7. #23781701 | C2 | semidirect |
| 8. #23781693 | C2 | semidirect |
| 11. #428×C163 | C2 | semidirect |
| 15. #19104734 | C22 | semidirect |
| 17. #19104726 | C22 | semidirect |
| 26. #19104668 | C22 | semidirect |
| 27. #19104668 | C22 | semidirect |
| 28. #19104666 | C22 | semidirect |
| 29. #19104666 | C22 | semidirect |
| 30. Dic163⋊C8 | C22 | semidirect |
| 31. Dic163⋊C8 | C22 | semidirect |
| 39. #107×C163 | C22 | semidirect |
| 40. #106×C163 | C22 | semidirect |
| 45. C2×D652 | Q8 | semidirect |
| 124. C163 | #3081 | semidirect |
| 132. #428 | D163 | semidirect |
| 156. #107 | C2×D163 | semidirect |
| 159. #106 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782296 | 2 |
| #23782139 | 2 |
| #23781968 | 2 |
| #23781964 | 2 |
| #23781954 | 2 |
| #23781944 | 2 |
| #23781701 | 2 |
| #23781693 | 2 |
| #23781671 | 2 |
| C2×#19104655 | 2 |
| #428×C163 | 2 |
| #3081 | 163 |