Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782479 | C2 | semidirect |
| 2. #23782477 | C2 | semidirect |
| 3. #23782467 | C2 | semidirect |
| 4. #23782049 | C2 | semidirect |
| 5. #23781941 | C2 | semidirect |
| 6. #23781936 | C2 | semidirect |
| 7. #23781928 | C2 | semidirect |
| 8. #23781844 | C2 | semidirect |
| 9. #23781839 | C2 | semidirect |
| 10. #23781783 | C2 | semidirect |
| 11. #443×C163 | C2 | semidirect |
| 12. #19104782 | C22 | semidirect |
| 16. #19104765 | C22 | semidirect |
| 19. #19104763 | C22 | semidirect |
| 26. C2×Dic652 | C22 | semidirect |
| 29. C2×#14579688 | C22 | semidirect |
| 33. #19104741 | C22 | semidirect |
| 34. #19104723 | C22 | semidirect |
| 35. #19104671 | C22 | semidirect |
| 37. #19104663 | C22 | semidirect |
| 38. #19104653 | C22 | semidirect |
| 39. #19104651 | C22 | semidirect |
| 41. #131×C163 | C22 | semidirect |
| 42. #108×C163 | C22 | semidirect |
| 43. #104×C163 | C22 | semidirect |
| 44. C4×C8×C163 | C22 | semidirect |
| 149. C163 | #3290 | semidirect |
| 161. #443 | D163 | semidirect |
| 185. #131 | C2×D163 | semidirect |
| 188. #108 | C2×D163 | semidirect |
| 191. #104 | C2×D163 | semidirect |
| 194. C4×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782479 | 2 |
| #23782477 | 2 |
| #23782467 | 2 |
| #23782049 | 2 |
| #23781941 | 2 |
| #23781936 | 2 |
| #23781928 | 2 |
| #23781844 | 2 |
| #23781839 | 2 |
| #23781783 | 2 |
| #443×C163 | 2 |
| #3290 | 163 |