Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. #23782006 | C2 | semidirect |
| 3. #23782000 | C2 | semidirect |
| 4. #23781995 | C2 | semidirect |
| 5. #23781989 | C2 | semidirect |
| 6. #23781983 | C2 | semidirect |
| 7. #23781978 | C2 | semidirect |
| 8. #23781701 | C2 | semidirect |
| 9. #23781659 | C2 | semidirect |
| 10. C2×C22⋊(C163⋊C8) | C2 | semidirect |
| 11. C2×#117×C163 | C2 | semidirect |
| 23. #19104668 | C22 | semidirect |
| 24. #19104668 | C22 | semidirect |
| 25. #19104666 | C22 | semidirect |
| 26. #19104666 | C22 | semidirect |
| 27. #19104658 | C22 | semidirect |
| 28. #19104658 | C22 | semidirect |
| 29. #19104655 | C22 | semidirect |
| 30. #19104655 | C22 | semidirect |
| 143. C163 | #3091 | semidirect |
| 146. C2×#117 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782176 | 2 |
| #23782006 | 2 |
| #23782000 | 2 |
| #23781995 | 2 |
| #23781989 | 2 |
| #23781983 | 2 |
| #23781978 | 2 |
| #23781701 | 2 |
| #23781659 | 2 |
| C2×C22⋊(C163⋊C8) | 2 |
| C2×#117×C163 | 2 |
| #3091 | 163 |