Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 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 |
|---|---|---|
| 2. C2×#19104766 | C2 | semidirect |
| 3. #23782239 | C2 | semidirect |
| 4. #23781826 | C2 | semidirect |
| 5. #23781819 | C2 | semidirect |
| 6. #23781674 | C2 | semidirect |
| 7. #23781662 | C2 | semidirect |
| 8. #23781631 | C2 | semidirect |
| 9. C22×Q16×C163 | C2 | semidirect |
| 140. C163 | #3011 | semidirect |
| 144. C22×Q16 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104783 | 2 |
| C2×#19104766 | 2 |
| #23782239 | 2 |
| #23781826 | 2 |
| #23781819 | 2 |
| #23781674 | 2 |
| #23781662 | 2 |
| #23781631 | 2 |
| C22×Q16×C163 | 2 |
| #3011 | 163 |