Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
448 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 127 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. #23782220 | C2 | semidirect |
| 3. #23781997 | C2 | semidirect |
| 4. #23781952 | C2 | semidirect |
| 5. #23781871 | C2 | semidirect |
| 6. #23781870 | C2 | semidirect |
| 8. #23781756 | C2 | semidirect |
| 9. #23781752 | C2 | semidirect |
| 10. #23781717 | C2 | semidirect |
| 11. #476×C163 | C2 | semidirect |
| 16. #19104735 | C22 | semidirect |
| 21. #19104700 | C22 | semidirect |
| 31. #19104666 | C22 | semidirect |
| 32. C4⋊(C163⋊C8) | C22 | semidirect |
| 33. #19104660 | C22 | semidirect |
| 34. #19104658 | C22 | semidirect |
| 37. C8×Dic163 | C22 | semidirect |
| 38. C4⋊Q8×C163 | C22 | semidirect |
| 40. #106×C163 | C22 | semidirect |
| 41. C4⋊C8×C163 | C22 | semidirect |
| 105. C4×D163 | SD16 | semidirect |
| 146. C163 | #3101 | semidirect |
| 152. #476 | D163 | semidirect |
| 164. C4⋊Q8 | C2×D163 | semidirect |
| 181. #106 | C2×D163 | semidirect |
| 183. C4⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782220 | 2 |
| C4×D4×D163 | 2 |
| #23781997 | 2 |
| #23781952 | 2 |
| #23781871 | 2 |
| #23781870 | 2 |
| #23781817 | 2 |
| #23781756 | 2 |
| #23781752 | 2 |
| #23781717 | 2 |
| #476×C163 | 2 |
| #3101 | 163 |