Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 1. C2×#19104768 | C2 | semidirect |
| 3. #23782236 | C2 | semidirect |
| 4. #23781923 | C2 | semidirect |
| 5. #23781911 | C2 | semidirect |
| 6. #23781906 | C2 | semidirect |
| 7. #23781894 | C2 | semidirect |
| 8. #23781707 | C2 | semidirect |
| 9. #23781662 | C2 | semidirect |
| 10. C2×#19104660 | C2 | semidirect |
| 11. C2×#131×C163 | C2 | semidirect |
| 79. M16×C163 | D4 | semidirect |
| 143. C163 | #3063 | semidirect |
| 146. C2×#131 | D163 | semidirect |
| 210. M16 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| #23782243 | 2 |
| #23782236 | 2 |
| #23781923 | 2 |
| #23781911 | 2 |
| #23781906 | 2 |
| #23781894 | 2 |
| #23781707 | 2 |
| #23781662 | 2 |
| C2×#19104660 | 2 |
| C2×#131×C163 | 2 |
| #3063 | 163 |