Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23782222 | C2 | semidirect |
| 3. #23781966 | C2 | semidirect |
| 4. #23781956 | C2 | semidirect |
| 5. #23781946 | C2 | semidirect |
| 6. #23781707 | C2 | semidirect |
| 8. #423×C163 | C2 | semidirect |
| 11. #19104735 | C22 | semidirect |
| 12. #19104735 | C22 | semidirect |
| 13. #19104727 | C22 | semidirect |
| 25. #19104669 | C22 | semidirect |
| 26. #19104667 | C22 | semidirect |
| 31. C4⋊C8×C163 | C22 | semidirect |
| 32. C4⋊C8×C163 | C22 | semidirect |
| 38. C2×D652 | Q8 | semidirect |
| 115. C163 | #3077 | semidirect |
| 123. #423 | D163 | semidirect |
| 145. C4⋊C8 | C2×D163 | semidirect |
| 146. C4⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782222 | 2 |
| C2×C4×D652 | 2 |
| #23781966 | 2 |
| #23781956 | 2 |
| #23781946 | 2 |
| #23781707 | 2 |
| #23781671 | 2 |
| #423×C163 | 2 |
| #3077 | 163 |