Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23781973 | C2 | semidirect |
| 4. #23781973 | C2 | semidirect |
| 5. #23781961 | C2 | semidirect |
| 6. #23781951 | C2 | semidirect |
| 44. C2×Dic326 | Q8 | semidirect |
| 116. C163 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782293 | 2 |
| #23782142 | 2 |
| #23781973 | 2 |
| #23781961 | 2 |
| #23781951 | 2 |
| #23781707 | 2 |
| #23781703 | 2 |
| #23781675 | 2 |
| C2×#19104660 | 2 |
| #424×C163 | 2 |
| #3082 | 163 |