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×#19104755 | C2 | semidirect |
| 2. C22×#14579682 | C2 | semidirect |
| 3. #23782177 | C2 | semidirect |
| 4. #23782172 | C2 | semidirect |
| 5. #23781922 | C2 | semidirect |
| 6. #23781917 | C2 | semidirect |
| 7. #23781914 | C2 | semidirect |
| 8. #23781910 | C2 | semidirect |
| 9. #23781701 | C2 | semidirect |
| 10. #23781662 | C2 | semidirect |
| 11. #416×C163 | C2 | semidirect |
| 15. C2×#14579689 | C22 | semidirect |
| 16. C2×#14579687 | C22 | semidirect |
| 17. C2×#14579686 | C22 | semidirect |
| 18. C2×#14579684 | C22 | semidirect |
| 34. #19104668 | C22 | semidirect |
| 35. #19104666 | C22 | semidirect |
| 36. #19104660 | C22 | semidirect |
| 37. #19104657 | C22 | semidirect |
| 41. #103×C163 | C22 | semidirect |
| 42. #102×C163 | C22 | semidirect |
| 63. C2×C163⋊C8 | D4 | semidirect |
| 148. C163 | #3054 | semidirect |
| 160. #416 | D163 | semidirect |
| 189. #103 | C2×D163 | semidirect |
| 191. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104755 | 2 |
| C22×#14579682 | 2 |
| #23782177 | 2 |
| #23782172 | 2 |
| #23781922 | 2 |
| #23781917 | 2 |
| #23781914 | 2 |
| #23781910 | 2 |
| #23781701 | 2 |
| #23781662 | 2 |
| #416×C163 | 2 |
| #3054 | 163 |