Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 490 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×#19104765 | C2 | semidirect |
| 2. C22×#14579688 | C2 | semidirect |
| 4. #23782142 | C2 | semidirect |
| 5. #23781890 | C2 | semidirect |
| 6. #23781864 | C2 | semidirect |
| 7. #23781691 | C2 | semidirect |
| 8. #23781669 | C2 | semidirect |
| 9. #416×C163 | C2 | semidirect |
| 13. C2×#14579689 | C22 | semidirect |
| 16. C2×#14579687 | C22 | semidirect |
| 23. #19104700 | C22 | semidirect |
| 26. Dic163⋊C8 | C22 | semidirect |
| 31. #103×C163 | C22 | semidirect |
| 32. #102×C163 | C22 | semidirect |
| 36. C2×Dic326 | D4 | semidirect |
| 116. C163 | #3043 | semidirect |
| 126. #416 | D163 | semidirect |
| 147. #103 | C2×D163 | semidirect |
| 149. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C22×#14579688 | 2 |
| #23782229 | 2 |
| #23782142 | 2 |
| #23781890 | 2 |
| #23781864 | 2 |
| #23781691 | 2 |
| #23781669 | 2 |
| #416×C163 | 2 |
| #3043 | 163 |