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. #23782476 | C2 | semidirect |
| 2. #23782475 | C2 | semidirect |
| 3. #23782037 | C2 | semidirect |
| 4. #23781927 | C2 | semidirect |
| 5. #23781926 | C2 | semidirect |
| 6. #23781849 | C2 | semidirect |
| 7. #23781832 | C2 | semidirect |
| 8. #23781779 | C2 | semidirect |
| 9. #453×C163 | C2 | semidirect |
| 11. #19104780 | C22 | semidirect |
| 12. #19104768 | C22 | semidirect |
| 14. #19104765 | C22 | semidirect |
| 23. C2×#14579687 | C22 | semidirect |
| 24. C2×#14579687 | C22 | semidirect |
| 26. #19104743 | C22 | semidirect |
| 27. #19104742 | C22 | semidirect |
| 28. #19104735 | C22 | semidirect |
| 29. #19104670 | C22 | semidirect |
| 30. #19104663 | C22 | semidirect |
| 31. #19104653 | C22 | semidirect |
| 32. #19104652 | C22 | semidirect |
| 33. C4×C163⋊C8 | C22 | semidirect |
| 34. H(5,𝔽2)×C163 | C22 | semidirect |
| 37. #104×C163 | C22 | semidirect |
| 38. #100×C163 | C22 | semidirect |
| 51. #14579689 | D4 | semidirect |
| 59. #14579687 | D4 | semidirect |
| 60. #14579686 | D4 | semidirect |
| 62. #14579684 | D4 | semidirect |
| 133. C163 | #3291 | semidirect |
| 142. #453 | D163 | semidirect |
| 146. H(5,𝔽2) | C2×D163 | semidirect |
| 168. #104 | C2×D163 | semidirect |
| 171. #100 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782476 | 2 |
| #23782475 | 2 |
| #23782037 | 2 |
| #23781927 | 2 |
| #23781926 | 2 |
| #23781849 | 2 |
| #23781832 | 2 |
| #23781779 | 2 |
| #453×C163 | 2 |
| #3291 | 163 |