Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19104763 | C2 | semidirect |
| 2. C2×#19104757 | C2 | semidirect |
| 3. #23782234 | C2 | semidirect |
| 4. #23782145 | C2 | semidirect |
| 5. #23781888 | C2 | semidirect |
| 6. #23781881 | C2 | semidirect |
| 7. #23781866 | C2 | semidirect |
| 8. #23781861 | C2 | semidirect |
| 9. #23781667 | C2 | semidirect |
| 10. C2×#19104657 | C2 | semidirect |
| 11. #424×C163 | C2 | semidirect |
| 17. C2×Dic652 | C22 | semidirect |
| 19. C2×#14579688 | C22 | semidirect |
| 20. C2×#14579688 | C22 | semidirect |
| 22. C2×D1304 | C22 | semidirect |
| 28. C4×Dic326 | C22 | semidirect |
| 29. C4×D652 | C22 | semidirect |
| 34. #19104660 | C22 | semidirect |
| 37. #19104657 | C22 | semidirect |
| 41. C4⋊C8×C163 | C22 | semidirect |
| 42. C4⋊C8×C163 | C22 | semidirect |
| 47. #14579699 | D4 | semidirect |
| 154. C163 | #3045 | semidirect |
| 164. #424 | D163 | semidirect |
| 192. C4⋊C8 | C2×D163 | semidirect |
| 193. C4⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104763 | 2 |
| C2×#19104757 | 2 |
| #23782234 | 2 |
| #23782145 | 2 |
| #23781888 | 2 |
| #23781881 | 2 |
| #23781866 | 2 |
| #23781861 | 2 |
| #23781667 | 2 |
| C2×#19104657 | 2 |
| #424×C163 | 2 |
| #3045 | 163 |