Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19104761 | C2 | semidirect |
| 2. C22×#14579684 | C2 | semidirect |
| 3. #23782234 | C2 | semidirect |
| 4. #23781880 | C2 | semidirect |
| 5. #23781860 | C2 | semidirect |
| 6. #23781692 | C2 | semidirect |
| 7. #23781669 | C2 | semidirect |
| 8. #23781659 | C2 | semidirect |
| 9. #518×C163 | C2 | semidirect |
| 13. C2×#14579687 | C22 | semidirect |
| 16. C2×#14579684 | C22 | semidirect |
| 19. #19104732 | C22 | semidirect |
| 20. #19104723 | C22 | semidirect |
| 23. C4⋊(C163⋊C8) | C22 | semidirect |
| 24. #19104658 | C22 | semidirect |
| 25. #19104655 | C22 | semidirect |
| 26. #19104655 | C22 | semidirect |
| 29. C4×D4×C163 | C22 | semidirect |
| 56. C2×D4×C163 | D4 | semidirect |
| 121. C163 | #3041 | semidirect |
| 126. #518 | D163 | semidirect |
| 147. C4×D4 | C2×D163 | semidirect |
| 169. C2×D4 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| C22×#14579684 | 2 |
| #23782234 | 2 |
| #23781880 | 2 |
| #23781860 | 2 |
| #23781692 | 2 |
| #23781669 | 2 |
| #23781659 | 2 |
| #518×C163 | 2 |
| #3041 | 163 |