Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #23781565 | C2 | semidirect |
| 3. #23781559 | C2 | semidirect |
| 4. #23781553 | C2 | semidirect |
| 5. #23781541 | C2 | semidirect |
| 6. #23781521 | C2 | semidirect |
| 7. #379×C163 | C2 | semidirect |
| 9. C22×C4×D163 | C22 | semidirect |
| 10. #19104704 | C4 | semidirect |
| 11. C2×Dic163⋊C4 | C22 | semidirect |
| 15. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 16. C2×C4×Dic163 | C22 | semidirect |
| 17. C163⋊#95 | C22 | semidirect |
| 18. C163⋊#95 | C22 | semidirect |
| 33. C22⋊Dic163 | C2×C4 | semidirect |
| 38. C24×C163 | C2×C4 | semidirect |
| 95. C163 | #2375 | semidirect |
| 103. #379 | D163 | semidirect |
| 121. C24 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104704 | 2 |
| #23781565 | 2 |
| #23781559 | 2 |
| #23781553 | 2 |
| #23781541 | 2 |
| #23781521 | 2 |
| #379×C163 | 2 |
| #2375 | 163 |