Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782221 | C2 | semidirect |
| 3. #23782026 | C2 | semidirect |
| 4. #23782023 | C2 | semidirect |
| 5. #23782022 | C2 | semidirect |
| 6. #23782020 | C2 | semidirect |
| 7. #23782019 | C2 | semidirect |
| 8. #23781672 | C2 | semidirect |
| 10. C4×#14579682 | C2 | semidirect |
| 11. #488×C163 | C2 | semidirect |
| 15. #19104734 | C22 | semidirect |
| 16. #19104727 | C22 | semidirect |
| 26. #19104660 | C22 | semidirect |
| 27. #19104659 | C22 | semidirect |
| 28. #19104658 | C22 | semidirect |
| 32. #19104645 | C22 | semidirect |
| 33. C4×C163⋊C8 | C22 | semidirect |
| 34. #125×C163 | C22 | semidirect |
| 36. #103×C163 | C22 | semidirect |
| 38. C4×C8×C163 | C22 | semidirect |
| 115. C163 | #3140 | semidirect |
| 124. #488 | D163 | semidirect |
| 133. #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 |
|---|---|
| #23782221 | 2 |
| #124×D163 | 2 |
| #23782026 | 2 |
| #23782023 | 2 |
| #23782022 | 2 |
| #23782020 | 2 |
| #23782019 | 2 |
| #23781672 | 2 |
| #23781668 | 2 |
| C4×#14579682 | 2 |
| #488×C163 | 2 |
| #3140 | 163 |