Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#19104735 | C2 | semidirect |
| 5. #23781673 | C2 | semidirect |
| 6. C2×#19104653 | C2 | semidirect |
| 7. #339×C163 | C2 | semidirect |
| 125. C163 | #2005 | semidirect |
| 133. #339 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| #23782241 | 2 |
| C2×#19104735 | 2 |
| C2×#19104663 | 2 |
| #23781673 | 2 |
| C2×#19104653 | 2 |
| #339×C163 | 2 |
| #2005 | 163 |