Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#19104761 | C2 | semidirect |
| 2. #23782215 | C2 | semidirect |
| 3. #23781880 | C2 | semidirect |
| 4. #23781870 | C2 | semidirect |
| 5. #23781860 | C2 | semidirect |
| 6. #23781689 | C2 | semidirect |
| 7. #23781664 | C2 | semidirect |
| 8. C2×C4×D4×C163 | C2 | semidirect |
| 14. #19104735 | C22 | semidirect |
| 15. #19104732 | C22 | semidirect |
| 16. #19104723 | C22 | semidirect |
| 21. C4⋊(C163⋊C8) | C22 | semidirect |
| 22. C4⋊(C163⋊C8) | C22 | semidirect |
| 23. #19104658 | C22 | semidirect |
| 24. #19104655 | C22 | semidirect |
| 53. C2×D4×C163 | D4 | semidirect |
| 119. C4×C163 | AGL(1,ℤ/8) | semidirect |
| 129. C163 | #3036 | semidirect |
| 133. C2×C4×D4 | D163 | semidirect |
| 174. C2×D4 | D652 | semidirect |
| 250. C4 | #19104761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| #23782215 | 2 |
| #23781880 | 2 |
| #23781870 | 2 |
| #23781860 | 2 |
| #23781689 | 2 |
| #23781664 | 2 |
| C2×C4×D4×C163 | 2 |
| #3036 | 163 |