Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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. #23782380 | C2 | semidirect |
| 2. #23782011 | C2 | semidirect |
| 3. #23781986 | C2 | semidirect |
| 4. #23781960 | C2 | semidirect |
| 5. #23781899 | C2 | semidirect |
| 6. #23781857 | C2 | semidirect |
| 7. #23781810 | C2 | semidirect |
| 8. C4×#14579686 | C2 | semidirect |
| 9. D4×C163⋊C8 | C2 | semidirect |
| 10. #23781661 | C2 | semidirect |
| 11. #550×C163 | C2 | semidirect |
| 132. C163 | #3305 | semidirect |
| 135. #550 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782380 | 2 |
| #23782011 | 2 |
| #23781986 | 2 |
| #23781960 | 2 |
| #23781899 | 2 |
| #23781857 | 2 |
| #23781810 | 2 |
| C4×#14579686 | 2 |
| D4×C163⋊C8 | 2 |
| #23781661 | 2 |
| #550×C163 | 2 |
| #3305 | 163 |