Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#19104718 | C2 | semidirect |
| 3. #23781580 | C2 | semidirect |
| 4. #23781544 | C2 | semidirect |
| 5. #23781537 | C2 | semidirect |
| 6. #23781521 | C2 | semidirect |
| 7. #23781520 | C2 | semidirect |
| 8. C22×C22⋊C4×C163 | C2 | semidirect |
| 16. C2×Dic163⋊C4 | C22 | semidirect |
| 18. C2×C22⋊Dic163 | C22 | semidirect |
| 19. C2×C22⋊Dic163 | C22 | semidirect |
| 20. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 21. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 22. C163⋊#95 | C22 | semidirect |
| 24. C23×C4×C163 | C22 | semidirect |
| 25. C23×C4×C163 | C22 | semidirect |
| 28. C2×C22⋊C4×C163 | C22 | semidirect |
| 119. C22×C163 | #123 | semidirect |
| 142. C163 | #2405 | semidirect |
| 146. C22×C22⋊C4 | D163 | semidirect |
| 159. C23×C4 | C2×D163 | semidirect |
| 160. C23×C4 | C2×D163 | semidirect |
| 170. C2×C22⋊C4 | C2×D163 | semidirect |
| 268. C22 | #19104718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D163 | 2 |
| C2×#19104718 | 2 |
| #23781580 | 2 |
| #23781544 | 2 |
| #23781537 | 2 |
| #23781521 | 2 |
| #23781520 | 2 |
| C22×C22⋊C4×C163 | 2 |
| #2405 | 163 |