Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 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 |
|---|---|---|
| 2. C2×#19104768 | C2 | semidirect |
| 3. C2×#19104765 | C2 | semidirect |
| 4. C2×#19104735 | C2 | semidirect |
| 5. #23781849 | C2 | direct (N × H) |
| 6. C2×#19104663 | C2 | semidirect |
| 7. C2×#19104653 | C2 | semidirect |
| 8. C2×#104×C163 | C2 | semidirect |
| 22. #19104768 | C22 | semidirect |
| 24. #19104765 | C22 | semidirect |
| 31. #19104735 | C22 | semidirect |
| 33. #19104663 | C22 | semidirect |
| 34. #19104653 | C22 | semidirect |
| 38. #104×C163 | C22 | semidirect |
| 167. C2×C163 | #456 | semidirect |
| 170. C163 | C2×#456 | semidirect |
| 178. C2×#104 | D163 | semidirect |
| 208. #104 | C2×D163 | semidirect |
| 339. C2 | #23781849 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104782 | 2 |
| C2×#19104768 | 2 |
| C2×#19104765 | 2 |
| C2×#19104735 | 2 |
| #23781849 | 2 |
| C2×#19104663 | 2 |
| C2×#19104653 | 2 |
| C2×#104×C163 | 2 |
| C2×#456 | 163 |