Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 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. #23782007 | C2 | direct (N × H) |
| 4. C2×#19104669 | C2 | semidirect |
| 5. C2×#19104667 | C2 | semidirect |
| 6. C2×#19104660 | C2 | semidirect |
| 7. C2×#19104660 | C2 | semidirect |
| 21. #19104669 | C22 | semidirect |
| 22. #19104667 | C22 | semidirect |
| 23. #19104660 | C22 | semidirect |
| 24. #19104660 | C22 | semidirect |
| 102. C2×C163 | #485 | semidirect |
| 106. C163 | C2×#485 | semidirect |
| 209. C2 | #23782007 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104714 | 2 |
| C2×#19104694 | 2 |
| #23782007 | 2 |
| C2×#19104669 | 2 |
| C2×#19104667 | 2 |
| C2×#19104660 | 2 |
| C2×C22⋊C8×C163 | 2 |
| C2×#485 | 163 |