Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19104780 | C2 | semidirect |
| 2. C2×#19104761 | C2 | semidirect |
| 3. #23782232 | C2 | semidirect |
| 4. #23781807 | C2 | semidirect |
| 5. #23781797 | C2 | semidirect |
| 6. #23781670 | C2 | semidirect |
| 7. #23781662 | C2 | semidirect |
| 8. #23781631 | C2 | semidirect |
| 9. C22×D8×C163 | C2 | semidirect |
| 15. C2×#14579698 | C22 | semidirect |
| 18. C2×D4×D163 | C22 | semidirect |
| 20. C2×#14579687 | C22 | semidirect |
| 21. C2×#14579684 | C22 | semidirect |
| 22. C2×#14579683 | C22 | semidirect |
| 25. #19104706 | C22 | semidirect |
| 27. #19104694 | C22 | semidirect |
| 28. #19104660 | C22 | semidirect |
| 29. #19104657 | C22 | semidirect |
| 30. #19104656 | C22 | semidirect |
| 31. (C2×D163)⋊C8 | C22 | semidirect |
| 33. C22×D4×C163 | C22 | semidirect |
| 35. C2×D8×C163 | C22 | semidirect |
| 36. C22×C8×C163 | C22 | semidirect |
| 41. #14579699 | D4 | semidirect |
| 76. C2×D4×C163 | D4 | semidirect |
| 151. C163 | #3008 | semidirect |
| 155. C22×D8 | D163 | semidirect |
| 172. C22×D4 | C2×D163 | semidirect |
| 177. C2×D8 | C2×D163 | semidirect |
| 179. C22×C8 | C2×D163 | semidirect |
| 217. C2×D4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104780 | 2 |
| C2×#19104761 | 2 |
| #23782232 | 2 |
| #23781807 | 2 |
| #23781797 | 2 |
| #23781670 | 2 |
| #23781662 | 2 |
| #23781631 | 2 |
| C22×D8×C163 | 2 |
| #3008 | 163 |