Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
786 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#19104718 | C2 | semidirect |
| 3. C2×#19104694 | C2 | semidirect |
| 4. #23781588 | C2 | semidirect |
| 5. #23781581 | C2 | semidirect |
| 6. #23781565 | C2 | semidirect |
| 7. #23781559 | C2 | semidirect |
| 8. #23781544 | C2 | semidirect |
| 9. #23781538 | C2 | semidirect |
| 10. #23781521 | C2 | semidirect |
| 11. C22×C22⋊C4×C163 | C2 | semidirect |
| 17. C2×C4⋊Dic163 | C22 | semidirect |
| 18. C2×Dic163⋊C4 | C22 | semidirect |
| 19. C2×Dic163⋊C4 | C22 | semidirect |
| 20. C2×Dic163⋊C4 | C22 | semidirect |
| 27. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 28. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 29. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 30. C2×C4×Dic163 | C22 | semidirect |
| 31. C163⋊#95 | C22 | semidirect |
| 32. C163⋊#95 | C22 | semidirect |
| 76. C22×C4×C163 | D4 | semidirect |
| 170. C163 | #2411 | semidirect |
| 175. C22×C22⋊C4 | D163 | semidirect |
| 233. C22×C4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104718 | 2 |
| C2×#19104704 | 2 |
| C2×#19104694 | 2 |
| #23781588 | 2 |
| #23781581 | 2 |
| #23781565 | 2 |
| #23781559 | 2 |
| #23781544 | 2 |
| #23781538 | 2 |
| #23781521 | 2 |
| C22×C22⋊C4×C163 | 2 |
| #2411 | 163 |