Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C2×#19104765 | C2 | semidirect |
| 2. C2×#19104741 | C2 | semidirect |
| 4. #23782241 | C2 | semidirect |
| 5. #23781922 | C2 | semidirect |
| 6. #23781910 | C2 | semidirect |
| 7. #23781905 | C2 | semidirect |
| 8. #23781893 | C2 | semidirect |
| 9. #23781708 | C2 | semidirect |
| 10. C2×#19104660 | C2 | semidirect |
| 11. #416×C163 | C2 | semidirect |
| 58. #14579683 | D4 | semidirect |
| 143. C163 | #3063 | semidirect |
| 154. #416 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C2×#19104741 | 2 |
| #23782243 | 2 |
| #23782241 | 2 |
| #23781922 | 2 |
| #23781910 | 2 |
| #23781905 | 2 |
| #23781893 | 2 |
| #23781708 | 2 |
| C2×#19104660 | 2 |
| #416×C163 | 2 |
| #3063 | 163 |