Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 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. C2×#19104758 | C2 | semidirect |
| 2. C2×D8×D163 | C2 | semidirect |
| 3. #23782308 | C2 | semidirect |
| 4. #23781903 | C2 | semidirect |
| 5. #23781898 | C2 | semidirect |
| 6. #23781877 | C2 | semidirect |
| 7. #23781814 | C2 | semidirect |
| 8. #23781809 | C2 | semidirect |
| 9. C4×D1304 | C2 | semidirect |
| 10. C8×D652 | C2 | semidirect |
| 11. #495×C163 | C2 | semidirect |
| 12. C2×#14579700 | C22 | semidirect |
| 15. C2×#14579686 | C22 | semidirect |
| 20. C2×C8×D163 | C22 | semidirect |
| 24. #19104706 | C22 | semidirect |
| 27. C4×D652 | C22 | semidirect |
| 29. #19104669 | C22 | semidirect |
| 30. C4⋊(C163⋊C8) | C22 | semidirect |
| 31. #19104659 | C22 | semidirect |
| 32. #19104657 | C22 | semidirect |
| 33. #19104656 | C22 | semidirect |
| 35. (C2×D163)⋊C8 | C22 | semidirect |
| 36. C2×Q16×C163 | C22 | semidirect |
| 37. C2×SD16×C163 | C22 | semidirect |
| 39. #124×C163 | C22 | semidirect |
| 40. C4×C8×C163 | C22 | semidirect |
| 56. D1304 | D4 | semidirect |
| 127. C2×D163 | #135 | semidirect |
| 143. C163 | #3280 | semidirect |
| 148. #495 | D163 | semidirect |
| 159. C2×Q16 | C2×D163 | semidirect |
| 161. C2×SD16 | C2×D163 | semidirect |
| 168. #124 | C2×D163 | semidirect |
| 184. C4×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| C2×D8×D163 | 2 |
| #23782308 | 2 |
| #23781903 | 2 |
| #23781898 | 2 |
| #23781877 | 2 |
| #23781814 | 2 |
| #23781809 | 2 |
| C4×D1304 | 2 |
| C8×D652 | 2 |
| #495×C163 | 2 |
| #3280 | 163 |