Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782027 | C2 | semidirect |
| 4. #23782025 | C2 | semidirect |
| 5. #23782024 | C2 | semidirect |
| 6. #23782021 | C2 | semidirect |
| 7. #23782018 | C2 | semidirect |
| 8. #23781672 | C2 | semidirect |
| 10. #23781617 | C2 | semidirect |
| 11. #489×C163 | C2 | semidirect |
| 15. #19104735 | C22 | semidirect |
| 16. #19104726 | C22 | semidirect |
| 30. #19104660 | C22 | semidirect |
| 31. #19104659 | C22 | semidirect |
| 32. #19104658 | C22 | semidirect |
| 36. #19104646 | C22 | semidirect |
| 37. C8×Dic163 | C22 | semidirect |
| 38. C4⋊Q8×C163 | C22 | semidirect |
| 40. #103×C163 | C22 | semidirect |
| 42. #97×C163 | C22 | semidirect |
| 138. C163 | #3140 | semidirect |
| 145. #489 | D163 | semidirect |
| 155. C4⋊Q8 | C2×D163 | semidirect |
| 174. #103 | C2×D163 | semidirect |
| 180. #97 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782220 | 2 |
| #124×D163 | 2 |
| #23782027 | 2 |
| #23782025 | 2 |
| #23782024 | 2 |
| #23782021 | 2 |
| #23782018 | 2 |
| #23781672 | 2 |
| #23781668 | 2 |
| #23781617 | 2 |
| #489×C163 | 2 |
| #3140 | 163 |