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 |
|---|---|---|
| 1. C2×#19104768 | C2 | semidirect |
| 2. C2×#19104743 | C2 | semidirect |
| 4. #23782241 | C2 | semidirect |
| 5. #23781924 | C2 | semidirect |
| 6. #23781912 | C2 | semidirect |
| 7. #23781907 | C2 | semidirect |
| 8. #23781895 | C2 | semidirect |
| 9. #23781659 | C2 | semidirect |
| 10. C2×#19104658 | C2 | semidirect |
| 11. #428×C163 | C2 | semidirect |
| 77. M16×C163 | D4 | semidirect |
| 143. C163 | #3063 | semidirect |
| 153. #428 | D163 | semidirect |
| 210. M16 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| C2×#19104743 | 2 |
| #23782246 | 2 |
| #23782241 | 2 |
| #23781924 | 2 |
| #23781912 | 2 |
| #23781907 | 2 |
| #23781895 | 2 |
| #23781659 | 2 |
| C2×#19104658 | 2 |
| #428×C163 | 2 |
| #3063 | 163 |