Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 2. #23782239 | C2 | semidirect |
| 3. #23782148 | C2 | semidirect |
| 4. #23781889 | C2 | semidirect |
| 5. #23781882 | C2 | semidirect |
| 6. #23781873 | C2 | semidirect |
| 7. #23781868 | C2 | semidirect |
| 8. #23781693 | C2 | semidirect |
| 9. #23781667 | C2 | semidirect |
| 10. C2×#19104659 | C2 | semidirect |
| 11. C2×#137×C163 | C2 | semidirect |
| 146. C163 | #3046 | semidirect |
| 148. C2×#137 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104755 | 2 |
| #23782239 | 2 |
| #23782148 | 2 |
| #23781889 | 2 |
| #23781882 | 2 |
| #23781873 | 2 |
| #23781868 | 2 |
| #23781693 | 2 |
| #23781667 | 2 |
| C2×#19104659 | 2 |
| C2×#137×C163 | 2 |
| #3046 | 163 |