Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 3. #23781623 | C2 | semidirect |
| 4. C2×C4×C163⋊C8 | C2 | semidirect |
| 5. #23781429 | C2 | semidirect |
| 6. #23781425 | C2 | semidirect |
| 9. #19104742 | C4 | semidirect |
| 16. #19104659 | C4 | semidirect |
| 17. #19104656 | C4 | semidirect |
| 24. #104×C163 | C4 | semidirect |
| 98. C163 | #1764 | semidirect |
| 118. #104 | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104742 | 2 |
| #23781661 | 2 |
| #23781623 | 2 |
| C2×C4×C163⋊C8 | 2 |
| #23781429 | 2 |
| #23781425 | 2 |
| C2×#104×C163 | 2 |
| #1764 | 163 |