Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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 |
|---|---|---|
| 1. C2×#19104761 | C2 | semidirect |
| 2. C2×#19104757 | C2 | semidirect |
| 3. #23782232 | C2 | semidirect |
| 4. #23782146 | C2 | semidirect |
| 5. #23781886 | C2 | semidirect |
| 6. #23781879 | C2 | semidirect |
| 7. #23781864 | C2 | semidirect |
| 8. #23781859 | C2 | semidirect |
| 9. #23781691 | C2 | semidirect |
| 10. #23781664 | C2 | semidirect |
| 11. C2×#102×C163 | C2 | semidirect |
| 16. C2×Dic652 | C22 | semidirect |
| 17. C2×#14579688 | C22 | semidirect |
| 18. C2×#14579688 | C22 | semidirect |
| 20. C2×D1304 | C22 | semidirect |
| 28. #19104700 | C22 | semidirect |
| 29. #19104697 | C22 | semidirect |
| 34. Dic163⋊C8 | C22 | semidirect |
| 35. Dic163⋊C8 | C22 | semidirect |
| 36. #19104658 | C22 | semidirect |
| 37. #19104655 | C22 | semidirect |
| 46. #14579699 | D4 | semidirect |
| 154. C163 | #3045 | semidirect |
| 166. C2×#102 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| C2×#19104757 | 2 |
| #23782232 | 2 |
| #23782146 | 2 |
| #23781886 | 2 |
| #23781879 | 2 |
| #23781864 | 2 |
| #23781859 | 2 |
| #23781691 | 2 |
| #23781664 | 2 |
| C2×#102×C163 | 2 |
| #3045 | 163 |