Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1088 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 173 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×#19104724 | C2 | semidirect |
| 3. C2×#19104711 | C2 | semidirect |
| 4. #23781580 | C2 | semidirect |
| 5. #23781568 | C2 | semidirect |
| 6. #23781567 | C2 | semidirect |
| 7. #23781520 | C2 | semidirect |
| 8. C4×(C2×D163)⋊C4 | C2 | semidirect |
| 9. C2×#124×C163 | C2 | semidirect |
| 19. C2×C4⋊Dic163 | C22 | semidirect |
| 20. C2×Dic163⋊C4 | C22 | semidirect |
| 21. C2×C22⋊Dic163 | C22 | semidirect |
| 24. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 25. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 26. C2×C4×Dic163 | C22 | semidirect |
| 27. C163⋊#95 | C22 | semidirect |
| 28. C22×Q8×C163 | C22 | semidirect |
| 31. C2×C22⋊C4×C163 | C22 | semidirect |
| 32. C2×C42×C163 | C22 | semidirect |
| 136. C2×D163 | #124 | semidirect |
| 151. C163 | #2435 | semidirect |
| 155. C2×#124 | D163 | semidirect |
| 163. C22×Q8 | C2×D163 | semidirect |
| 181. C2×C22⋊C4 | C2×D163 | semidirect |
| 183. C2×C42 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D163 | 2 |
| C2×#19104724 | 2 |
| C2×#19104711 | 2 |
| #23781580 | 2 |
| #23781568 | 2 |
| #23781567 | 2 |
| #23781520 | 2 |
| C4×(C2×D163)⋊C4 | 2 |
| C2×#124×C163 | 2 |
| #2435 | 163 |