Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 3. #23781997 | C2 | direct (N × H) |
| 4. C2×#19104666 | C2 | semidirect |
| 5. C2×#19104660 | C2 | semidirect |
| 6. C2×#19104658 | C2 | semidirect |
| 8. C2×#106×C163 | C2 | semidirect |
| 21. #19104666 | C22 | semidirect |
| 22. #19104660 | C22 | semidirect |
| 23. #19104658 | C22 | semidirect |
| 28. #106×C163 | C22 | semidirect |
| 103. C2×C163 | #483 | semidirect |
| 108. C163 | C2×#483 | semidirect |
| 114. C2×#106 | D163 | semidirect |
| 134. #106 | C2×D163 | semidirect |
| 213. C2 | #23781997 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104715 | 2 |
| C2×C4⋊C4×D163 | 2 |
| #23781997 | 2 |
| C2×#19104666 | 2 |
| C2×#19104660 | 2 |
| C2×#19104658 | 2 |
| C2×(C2×D163)⋊C8 | 2 |
| C2×#106×C163 | 2 |
| C2×#483 | 163 |