Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23782139 | C2 | semidirect |
| 2. #23781986 | C2 | semidirect |
| 3. #23781962 | C2 | semidirect |
| 4. #23781857 | C2 | semidirect |
| 5. #23781798 | C2 | semidirect |
| 6. #23781775 | C2 | semidirect |
| 7. C4×#14579684 | C2 | semidirect |
| 8. #23781726 | C2 | semidirect |
| 9. #540×C163 | C2 | semidirect |
| 18. #19104668 | C22 | semidirect |
| 19. #19104666 | C22 | semidirect |
| 20. C4⋊(C163⋊C8) | C22 | semidirect |
| 21. #19104656 | C22 | semidirect |
| 22. #19104656 | C22 | semidirect |
| 26. #19104646 | C22 | semidirect |
| 27. C4×C163⋊C8 | C22 | semidirect |
| 28. #127×C163 | C22 | semidirect |
| 29. #125×C163 | C22 | semidirect |
| 33. C4×D4×C163 | C22 | semidirect |
| 108. C163 | #3122 | semidirect |
| 110. #540 | D163 | semidirect |
| 122. #127 | C2×D163 | semidirect |
| 123. #125 | C2×D163 | semidirect |
| 130. C4×D4 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782139 | 2 |
| #23781986 | 2 |
| #23781962 | 2 |
| #23781857 | 2 |
| #23781798 | 2 |
| #23781775 | 2 |
| C4×#14579684 | 2 |
| #23781726 | 2 |
| #540×C163 | 2 |
| #3122 | 163 |