Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 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. #23782482 | C2 | semidirect |
| 2. #23782475 | C2 | semidirect |
| 3. #23782466 | C2 | semidirect |
| 4. #23782048 | C2 | semidirect |
| 5. #23781941 | C2 | semidirect |
| 6. #23781927 | C2 | semidirect |
| 7. #23781845 | C2 | semidirect |
| 8. #23781836 | C2 | semidirect |
| 9. #23781781 | C2 | semidirect |
| 10. #23781780 | C2 | semidirect |
| 11. #472×C163 | C2 | semidirect |
| 12. #19104782 | C22 | semidirect |
| 16. #19104768 | C22 | semidirect |
| 27. C2×Dic652 | C22 | semidirect |
| 28. C2×#14579687 | C22 | semidirect |
| 31. #19104743 | C22 | semidirect |
| 33. #19104722 | C22 | semidirect |
| 34. #19104670 | C22 | semidirect |
| 35. #19104662 | C22 | semidirect |
| 37. #19104661 | C22 | semidirect |
| 38. #19104653 | C22 | semidirect |
| 39. C8×Dic163 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C163 | C22 | semidirect |
| 42. #131×C163 | C22 | semidirect |
| 43. #108×C163 | C22 | semidirect |
| 44. #100×C163 | C22 | semidirect |
| 149. C163 | #3290 | semidirect |
| 156. #472 | D163 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D163 | semidirect |
| 185. #131 | C2×D163 | semidirect |
| 188. #108 | C2×D163 | semidirect |
| 193. #100 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782482 | 2 |
| #23782475 | 2 |
| #23782466 | 2 |
| #23782048 | 2 |
| #23781941 | 2 |
| #23781927 | 2 |
| #23781845 | 2 |
| #23781836 | 2 |
| #23781781 | 2 |
| #23781780 | 2 |
| #472×C163 | 2 |
| #3290 | 163 |