Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14579698 | C2 | semidirect |
| 2. C2×#19104754 | C2 | semidirect |
| 3. #23782175 | C2 | semidirect |
| 4. #23781828 | C2 | semidirect |
| 5. #23781823 | C2 | semidirect |
| 6. #23781816 | C2 | semidirect |
| 7. #23781807 | C2 | semidirect |
| 8. #23781803 | C2 | semidirect |
| 9. #23781658 | C2 | semidirect |
| 10. C22⋊C8×D163 | C2 | semidirect |
| 11. #447×C163 | C2 | semidirect |
| 17. C2×#14579698 | C22 | semidirect |
| 23. C2×Dic652 | C22 | semidirect |
| 24. C2×#14579687 | C22 | semidirect |
| 25. C2×#14579687 | C22 | semidirect |
| 26. C2×C8×D163 | C22 | semidirect |
| 28. #19104715 | C22 | semidirect |
| 30. #19104706 | C22 | semidirect |
| 34. #19104693 | C22 | semidirect |
| 35. #19104660 | C22 | semidirect |
| 36. #19104658 | C22 | semidirect |
| 37. #19104656 | C22 | semidirect |
| 39. (C2×D163)⋊C8 | C22 | semidirect |
| 41. C2×D8×C163 | C22 | semidirect |
| 43. #102×C163 | C22 | semidirect |
| 52. #14579698 | D4 | semidirect |
| 150. C22×C163 | #135 | semidirect |
| 175. C163 | #3002 | semidirect |
| 185. #447 | D163 | semidirect |
| 203. C2×D8 | C2×D163 | semidirect |
| 217. #102 | C2×D163 | semidirect |
| 333. C22 | #19104754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579698 | 2 |
| C2×#19104754 | 2 |
| #23782175 | 2 |
| #23781828 | 2 |
| #23781823 | 2 |
| #23781816 | 2 |
| #23781807 | 2 |
| #23781803 | 2 |
| #23781658 | 2 |
| C22⋊C8×D163 | 2 |
| #447×C163 | 2 |
| #3002 | 163 |