Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782471 | C2 | semidirect |
| 2. #23781925 | C2 | semidirect |
| 3. #23781847 | C2 | semidirect |
| 4. #23781832 | C2 | semidirect |
| 5. #23781783 | C2 | semidirect |
| 6. #492×C163 | C2 | semidirect |
| 8. #19104780 | C22 | semidirect |
| 9. #19104766 | C22 | semidirect |
| 16. #19104741 | C22 | semidirect |
| 17. #19104671 | C22 | semidirect |
| 18. #19104663 | C22 | semidirect |
| 19. #19104654 | C22 | semidirect |
| 20. #19104652 | C22 | semidirect |
| 21. C2×SD16×C163 | C22 | semidirect |
| 22. C4⋊Q8×C163 | C22 | semidirect |
| 24. C4×C8×C163 | C22 | semidirect |
| 32. Dic652 | D4 | semidirect |
| 34. #14579688 | D4 | semidirect |
| 37. D1304 | D4 | semidirect |
| 83. C163 | #3291 | semidirect |
| 86. #492 | D163 | semidirect |
| 100. C2×SD16 | C2×D163 | semidirect |
| 102. C4⋊Q8 | C2×D163 | semidirect |
| 108. C4×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782471 | 2 |
| #23781925 | 2 |
| #23781847 | 2 |
| #23781832 | 2 |
| #23781783 | 2 |
| #492×C163 | 2 |
| #3291 | 163 |