Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
412 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 125 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. #125×D163 | C2 | semidirect |
| 3. #23782022 | C2 | semidirect |
| 4. #23782021 | C2 | semidirect |
| 5. #23782020 | C2 | semidirect |
| 6. #23782019 | C2 | semidirect |
| 7. #23782018 | C2 | semidirect |
| 8. #103×D163 | C2 | semidirect |
| 10. C4×C8×D163 | C2 | semidirect |
| 11. #488×C163 | C2 | semidirect |
| 15. #19104727 | C22 | semidirect |
| 16. #19104726 | C22 | semidirect |
| 26. #19104660 | C22 | semidirect |
| 27. #19104659 | C22 | semidirect |
| 28. #19104658 | C22 | semidirect |
| 32. C4×C163⋊C8 | C22 | semidirect |
| 33. C8×Dic163 | C22 | semidirect |
| 34. #125×C163 | C22 | semidirect |
| 36. #103×C163 | C22 | semidirect |
| 38. C4×C8×C163 | C22 | semidirect |
| 114. D163 | #488 | direct (N × H) |
| 115. C163 | C2×#488 | semidirect |
| 124. #488 | D163 | direct (N × H) |
| 134. #125 | C2×D163 | semidirect |
| 147. #103 | C2×D163 | semidirect |
| 154. C4×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D163 | 2 |
| #124×D163 | 2 |
| #23782022 | 2 |
| #23782021 | 2 |
| #23782020 | 2 |
| #23782019 | 2 |
| #23782018 | 2 |
| #103×D163 | 2 |
| #102×D163 | 2 |
| C4×C8×D163 | 2 |
| #488×C163 | 2 |
| C2×#488 | 163 |