Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×C4×Dic163 | C2 | semidirect |
| 3. C2×#19104661 | C2 | semidirect |
| 4. #23781426 | C2 | semidirect |
| 5. #407×C163 | C2 | semidirect |
| 9. #19104714 | C4 | semidirect |
| 10. #19104709 | C4 | semidirect |
| 23. C2×Dic326 | C2×C4 | semidirect |
| 24. C2×D652 | C2×C4 | semidirect |
| 31. C4⋊Dic163 | C2×C4 | semidirect |
| 39. C4×Dic163 | D4 | semidirect |
| 82. C22×C163 | #104 | semidirect |
| 100. C163 | #1896 | semidirect |
| 105. #407 | D163 | semidirect |
| 185. C22 | #19104661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782176 | 2 |
| C22×C4×Dic163 | 2 |
| C2×#19104661 | 2 |
| #23781426 | 2 |
| #407×C163 | 2 |
| #1896 | 163 |