Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782067 | C2 | semidirect |
| 3. #23782045 | C2 | semidirect |
| 4. #23782034 | C2 | semidirect |
| 7. #23781773 | C2 | semidirect |
| 8. C4×Dic652 | C2 | semidirect |
| 78. C163 | #3177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782277 | 2 |
| #23782067 | 2 |
| #23782045 | 2 |
| #23782034 | 2 |
| #23781923 | 2 |
| #23781906 | 2 |
| #23781773 | 2 |
| C4×Dic652 | 2 |
| #405×C163 | 2 |
| #3177 | 163 |