Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
994 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×D4×D163 | C2 | semidirect |
| 2. C2×#19104762 | C2 | semidirect |
| 3. #23782178 | C2 | semidirect |
| 4. #23781815 | C2 | semidirect |
| 5. #23781814 | C2 | semidirect |
| 6. #23781801 | C2 | semidirect |
| 7. #23781800 | C2 | semidirect |
| 8. #23781799 | C2 | semidirect |
| 9. #23781668 | C2 | semidirect |
| 10. #23781627 | C2 | semidirect |
| 11. #450×C163 | C2 | semidirect |
| 13. C2×#14579700 | C22 | semidirect |
| 23. C2×#14579686 | C22 | semidirect |
| 24. C2×D1304 | C22 | semidirect |
| 25. C2×#14579684 | C22 | semidirect |
| 26. C2×#14579682 | C22 | semidirect |
| 28. #19104711 | C22 | semidirect |
| 29. #19104710 | C22 | semidirect |
| 30. #19104709 | C22 | semidirect |
| 34. #19104693 | C22 | semidirect |
| 35. #19104657 | C22 | semidirect |
| 36. #19104656 | C22 | semidirect |
| 37. #19104655 | C22 | semidirect |
| 38. C22⋊(C163⋊C8) | C22 | semidirect |
| 39. (C2×D163)⋊C8 | C22 | semidirect |
| 41. C2×SD16×C163 | C22 | semidirect |
| 42. C22⋊Q8×C163 | C22 | semidirect |
| 43. #102×C163 | C22 | semidirect |
| 44. C22⋊C8×C163 | C22 | semidirect |
| 58. C2×D652 | C23 | semidirect |
| 68. D4×D163 | D4 | semidirect |
| 80. C2×C163⋊C8 | C23 | semidirect |
| 81. C4⋊Dic163 | C23 | semidirect |
| 89. C2×Q8×C163 | C23 | semidirect |
| 95. C2×C8×C163 | C23 | semidirect |
| 97. C4⋊C4×C163 | C23 | semidirect |
| 156. C22×C163 | AGL(1,ℤ/8) | semidirect |
| 173. C2×D163 | AGL(1,ℤ/8) | semidirect |
| 190. C163 | #3003 | semidirect |
| 197. #450 | D163 | semidirect |
| 216. C2×SD16 | C2×D163 | semidirect |
| 222. C22⋊Q8 | C2×D163 | semidirect |
| 232. #102 | C2×D163 | semidirect |
| 235. C22⋊C8 | C2×D163 | semidirect |
| 245. C2×Q8 | C22×D163 | semidirect |
| 279. C2×C8 | C22×D163 | semidirect |
| 283. C4⋊C4 | C22×D163 | semidirect |
| 363. C22 | #19104762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D163 | 2 |
| C2×#19104762 | 2 |
| #23782178 | 2 |
| #23781815 | 2 |
| #23781814 | 2 |
| #23781801 | 2 |
| #23781800 | 2 |
| #23781799 | 2 |
| #23781668 | 2 |
| #23781627 | 2 |
| #450×C163 | 2 |
| #3003 | 163 |