Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19104726 | C2 | semidirect |
| 3. #23781968 | C2 | direct (N × H) |
| 4. C2×#19104666 | C2 | semidirect |
| 5. C2×Dic163⋊C8 | C2 | semidirect |
| 8. C2×#107×C163 | C2 | semidirect |
| 13. #19104726 | C22 | semidirect |
| 21. #19104666 | C22 | semidirect |
| 22. Dic163⋊C8 | C22 | semidirect |
| 28. #107×C163 | C22 | semidirect |
| 98. C2×C163 | #478 | semidirect |
| 103. C163 | C2×#478 | semidirect |
| 108. C2×#107 | D163 | semidirect |
| 128. #107 | C2×D163 | semidirect |
| 203. C2 | #23781968 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104726 | 2 |
| C2×#19104697 | 2 |
| #23781968 | 2 |
| C2×#19104666 | 2 |
| C2×Dic163⋊C8 | 2 |
| C2×#19104657 | 2 |
| C2×#19104655 | 2 |
| C2×#107×C163 | 2 |
| C2×#478 | 163 |