Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 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×#19104768 | C2 | semidirect |
| 3. C2×#19104722 | C2 | semidirect |
| 4. #23782133 | C2 | semidirect |
| 5. #23781886 | C2 | semidirect |
| 6. #23781879 | C2 | semidirect |
| 7. #23781688 | C2 | semidirect |
| 8. #23781673 | C2 | semidirect |
| 9. #418×C163 | C2 | semidirect |
| 14. C2×Dic652 | C22 | semidirect |
| 15. C2×#14579688 | C22 | semidirect |
| 22. #19104700 | C22 | semidirect |
| 23. #19104697 | C22 | semidirect |
| 29. Dic163⋊C8 | C22 | semidirect |
| 30. #19104658 | C22 | semidirect |
| 125. C163 | #3040 | semidirect |
| 135. #418 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| C2×#19104761 | 2 |
| C2×#19104722 | 2 |
| #23782133 | 2 |
| #23781886 | 2 |
| #23781879 | 2 |
| #23781688 | 2 |
| #23781673 | 2 |
| #418×C163 | 2 |
| #3040 | 163 |