Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23782293 | C2 | semidirect |
| 2. #23781965 | C2 | semidirect |
| 3. #23781965 | C2 | semidirect |
| 4. #23781955 | C2 | semidirect |
| 5. #23781945 | C2 | semidirect |
| 6. #23781708 | C2 | semidirect |
| 7. #23781701 | C2 | semidirect |
| 8. #23781692 | C2 | semidirect |
| 14. #19104735 | C22 | semidirect |
| 16. #19104727 | C22 | semidirect |
| 21. #19104668 | C22 | semidirect |
| 22. #19104668 | C22 | semidirect |
| 23. #19104668 | C22 | semidirect |
| 24. #19104666 | C22 | semidirect |
| 25. #19104666 | C22 | semidirect |
| 26. #19104666 | C22 | semidirect |
| 27. C4⋊(C163⋊C8) | C22 | semidirect |
| 28. C4⋊(C163⋊C8) | C22 | semidirect |
| 60. C2×D4×C163 | Q8 | semidirect |
| 124. C163 | #3081 | semidirect |
| 170. C2×D4 | Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782293 | 2 |
| #23781965 | 2 |
| #23781955 | 2 |
| #23781945 | 2 |
| #23781708 | 2 |
| #23781701 | 2 |
| #23781692 | 2 |
| #23781670 | 2 |
| C2×#19104656 | 2 |
| #518×C163 | 2 |
| #3081 | 163 |