Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 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×#19104783 | C2 | semidirect |
| 2. C2×#19104761 | C2 | semidirect |
| 3. #23781837 | C2 | direct (N × H) |
| 4. C2×#19104663 | C2 | semidirect |
| 5. C2×#19104654 | C2 | semidirect |
| 6. C2×#124×C163 | C2 | semidirect |
| 9. #19104783 | C22 | semidirect |
| 15. #19104761 | C22 | semidirect |
| 19. #19104663 | C22 | semidirect |
| 20. #19104654 | C22 | semidirect |
| 24. #124×C163 | C22 | semidirect |
| 114. C2×C163 | #454 | semidirect |
| 117. C163 | C2×#454 | semidirect |
| 121. C2×#124 | D163 | semidirect |
| 140. #124 | C2×D163 | semidirect |
| 233. C2 | #23781837 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104783 | 2 |
| C2×#19104761 | 2 |
| #23781837 | 2 |
| C2×#19104663 | 2 |
| C2×#19104654 | 2 |
| C2×#124×C163 | 2 |
| C2×#454 | 163 |