Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. C2×#19104654 | C2 | semidirect |
| 4. #23781421 | C2 | semidirect |
| 5. #519×C163 | C2 | semidirect |
| 8. #19104733 | C4 | semidirect |
| 9. #19104724 | C4 | semidirect |
| 81. C163 | #1912 | semidirect |
| 84. #519 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782239 | 2 |
| #23781683 | 2 |
| C2×#19104654 | 2 |
| #23781421 | 2 |
| #519×C163 | 2 |
| #1912 | 163 |