Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D163 | C2 | semidirect |
| 4. #23781876 | C2 | semidirect |
| 5. #23781874 | C2 | semidirect |
| 6. #23781872 | C2 | semidirect |
| 7. #23781870 | C2 | semidirect |
| 8. #23781868 | C2 | semidirect |
| 9. #23781687 | C2 | semidirect |
| 10. #23781672 | C2 | semidirect |
| 11. #461×C163 | C2 | semidirect |
| 131. C4×C163 | #137 | semidirect |
| 139. Dic163 | #137 | semidirect |
| 145. C163 | #3039 | semidirect |
| 155. #461 | D163 | semidirect |
| 283. C4 | #19104764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104764 | 2 |
| C4⋊Q8×D163 | 2 |
| C4×#14579698 | 2 |
| #23781876 | 2 |
| #23781874 | 2 |
| #23781872 | 2 |
| #23781870 | 2 |
| #23781868 | 2 |
| #23781687 | 2 |
| #23781672 | 2 |
| #461×C163 | 2 |
| #3039 | 163 |