Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #23782148 | C2 | semidirect |
| 3. #23781990 | C2 | semidirect |
| 4. #23781990 | C2 | semidirect |
| 5. #23781984 | C2 | semidirect |
| 6. #23781979 | C2 | semidirect |
| 7. #23781707 | C2 | semidirect |
| 8. #23781703 | C2 | semidirect |
| 9. #23781671 | C2 | semidirect |
| 10. C2×#19104657 | C2 | semidirect |
| 11. #408×C163 | C2 | semidirect |
| 23. #19104694 | C22 | semidirect |
| 25. C2×C4⋊Dic163 | 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. C22⋊C8×C163 | C22 | semidirect |
| 40. C22⋊C8×C163 | C22 | semidirect |
| 134. C163 | #3096 | semidirect |
| 146. #408 | D163 | semidirect |
| 174. C22⋊C8 | C2×D163 | semidirect |
| 175. C22⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782229 | 2 |
| #23782148 | 2 |
| #23781990 | 2 |
| #23781984 | 2 |
| #23781979 | 2 |
| #23781707 | 2 |
| #23781703 | 2 |
| #23781671 | 2 |
| C2×#19104657 | 2 |
| #408×C163 | 2 |
| #3096 | 163 |