Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23782501 | C2 | semidirect |
| 2. C2×#19104763 | C2 | semidirect |
| 3. #23782229 | C2 | semidirect |
| 4. #23781840 | C2 | semidirect |
| 5. #23781835 | C2 | semidirect |
| 6. #23781681 | C2 | semidirect |
| 7. #413×C163 | C2 | semidirect |
| 8. #19104783 | C22 | semidirect |
| 12. #19104780 | C22 | semidirect |
| 16. C22×D652 | C22 | semidirect |
| 18. #19104763 | C22 | semidirect |
| 21. #19104731 | C22 | semidirect |
| 22. #19104724 | C22 | semidirect |
| 25. #19104694 | C22 | semidirect |
| 26. #19104661 | C22 | semidirect |
| 28. C2×M16×C163 | C22 | semidirect |
| 29. #101×C163 | C22 | semidirect |
| 30. #100×C163 | C22 | semidirect |
| 38. #14579699 | D4 | semidirect |
| 43. C2×Dic326 | D4 | semidirect |
| 49. C2×D652 | D4 | semidirect |
| 134. C163 | #3021 | semidirect |
| 142. #413 | D163 | semidirect |
| 157. C2×M16 | C2×D163 | semidirect |
| 164. #101 | C2×D163 | semidirect |
| 165. #100 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782501 | 2 |
| C2×#19104763 | 2 |
| #23782229 | 2 |
| #23781840 | 2 |
| #23781835 | 2 |
| #23781681 | 2 |
| #413×C163 | 2 |
| #3021 | 163 |