Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #23782293 | C2 | semidirect |
| 3. #23781966 | C2 | semidirect |
| 4. #23781966 | C2 | semidirect |
| 5. #23781956 | C2 | semidirect |
| 6. #23781946 | C2 | semidirect |
| 7. #23781707 | C2 | semidirect |
| 8. #23781703 | C2 | semidirect |
| 11. #424×C163 | C2 | semidirect |
| 13. #19104735 | C22 | semidirect |
| 15. #19104727 | C22 | semidirect |
| 26. #19104669 | C22 | semidirect |
| 27. #19104669 | C22 | semidirect |
| 28. #19104669 | C22 | semidirect |
| 29. #19104667 | C22 | semidirect |
| 30. #19104667 | C22 | semidirect |
| 31. #19104667 | C22 | semidirect |
| 39. C4⋊C8×C163 | C22 | semidirect |
| 40. C4⋊C8×C163 | C22 | semidirect |
| 45. C2×D652 | Q8 | semidirect |
| 124. C163 | #3081 | semidirect |
| 134. #424 | D163 | semidirect |
| 160. C4⋊C8 | C2×D163 | semidirect |
| 161. C4⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782293 | 2 |
| #23782139 | 2 |
| #23781966 | 2 |
| #23781956 | 2 |
| #23781946 | 2 |
| #23781707 | 2 |
| #23781703 | 2 |
| #23781671 | 2 |
| C2×#19104657 | 2 |
| #424×C163 | 2 |
| #3081 | 163 |