Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782375 | C2 | semidirect |
| 3. #23782011 | C2 | semidirect |
| 4. #23781982 | C2 | semidirect |
| 5. #23781956 | C2 | semidirect |
| 6. #23781891 | C2 | semidirect |
| 7. #23781814 | C2 | semidirect |
| 8. C4×#14579686 | C2 | semidirect |
| 9. #23781730 | C2 | semidirect |
| 10. #102×D163 | C2 | semidirect |
| 11. #460×C163 | C2 | semidirect |
| 15. C2×C8×D163 | C22 | semidirect |
| 16. #19104735 | C22 | semidirect |
| 19. #19104711 | C22 | semidirect |
| 26. C4⋊C4×D163 | C22 | semidirect |
| 27. #19104667 | C22 | semidirect |
| 28. #19104666 | C22 | semidirect |
| 29. #19104659 | C22 | semidirect |
| 31. #19104656 | C22 | semidirect |
| 32. #19104656 | C22 | semidirect |
| 34. (C2×D163)⋊C8 | C22 | semidirect |
| 35. C4×C163⋊C8 | C22 | semidirect |
| 36. C2×SD16×C163 | C22 | semidirect |
| 38. C4×Q8×C163 | C22 | semidirect |
| 39. C4⋊C8×C163 | C22 | semidirect |
| 40. #102×C163 | C22 | semidirect |
| 84. D652 | SD16 | semidirect |
| 136. C163 | #3295 | semidirect |
| 144. #460 | D163 | semidirect |
| 152. C2×SD16 | C2×D163 | semidirect |
| 162. C4×Q8 | C2×D163 | semidirect |
| 169. C4⋊C8 | C2×D163 | semidirect |
| 175. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782375 | 2 |
| #23782300 | 2 |
| #23782011 | 2 |
| #23781982 | 2 |
| #23781956 | 2 |
| #23781891 | 2 |
| #23781814 | 2 |
| C4×#14579686 | 2 |
| #23781730 | 2 |
| #102×D163 | 2 |
| #460×C163 | 2 |
| #3295 | 163 |