Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #23782220 | C2 | semidirect |
| 3. #23782028 | C2 | semidirect |
| 4. #23782013 | C2 | semidirect |
| 5. #23782012 | C2 | semidirect |
| 6. #23782011 | C2 | semidirect |
| 7. #23781668 | C2 | semidirect |
| 8. C4×#14579682 | C2 | semidirect |
| 9. #486×C163 | C2 | semidirect |
| 14. #19104735 | C22 | semidirect |
| 19. #19104726 | C22 | semidirect |
| 26. #19104657 | C22 | semidirect |
| 27. #19104656 | C22 | semidirect |
| 28. #19104655 | C22 | semidirect |
| 29. #19104645 | C22 | semidirect |
| 30. C4×C163⋊C8 | C22 | semidirect |
| 31. C4⋊Q8×C163 | C22 | semidirect |
| 33. #102×C163 | C22 | semidirect |
| 34. C4×C8×C163 | C22 | semidirect |
| 123. C163 | #3138 | semidirect |
| 131. #486 | D163 | semidirect |
| 139. C4⋊Q8 | C2×D163 | semidirect |
| 155. #102 | C2×D163 | semidirect |
| 158. C4×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782220 | 2 |
| #127×D163 | 2 |
| #23782028 | 2 |
| #23782013 | 2 |
| #23782012 | 2 |
| #23782011 | 2 |
| #23781668 | 2 |
| C4×#14579682 | 2 |
| #486×C163 | 2 |
| #3138 | 163 |