Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
448 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23782217 | C2 | semidirect |
| 3. #23781996 | C2 | semidirect |
| 4. #23781993 | C2 | semidirect |
| 5. #23781953 | C2 | semidirect |
| 6. #23781868 | C2 | semidirect |
| 8. #23781756 | C2 | semidirect |
| 9. SD16×Dic163 | C2 | semidirect |
| 10. #23781715 | C2 | semidirect |
| 14. #19104734 | C22 | semidirect |
| 15. #19104733 | C22 | semidirect |
| 19. Q8×Dic163 | C22 | semidirect |
| 21. #19104700 | C22 | semidirect |
| 30. #19104667 | C22 | semidirect |
| 31. #19104666 | C22 | semidirect |
| 32. Dic163⋊C8 | C22 | semidirect |
| 33. #19104660 | C22 | semidirect |
| 34. #19104659 | C22 | semidirect |
| 37. C8×Dic163 | C22 | semidirect |
| 91. C2×Dic163 | SD16 | semidirect |
| 136. C163 | #3101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782217 | 2 |
| C2×D4×Dic163 | 2 |
| #23781996 | 2 |
| #23781993 | 2 |
| #23781953 | 2 |
| #23781868 | 2 |
| #23781816 | 2 |
| #23781756 | 2 |
| SD16×Dic163 | 2 |
| #23781715 | 2 |
| #450×C163 | 2 |
| #3101 | 163 |