Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #23781673 | C2 | semidirect |
| 5. #23781571 | C2 | semidirect |
| 6. #23781433 | C2 | semidirect |
| 7. #339×C163 | C2 | semidirect |
| 11. #19104768 | C4 | semidirect |
| 37. C2×Dic326 | C2×C4 | semidirect |
| 58. M16×C163 | C2×C4 | semidirect |
| 124. C163 | #1882 | semidirect |
| 132. #339 | D163 | semidirect |
| 177. M16 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104768 | 2 |
| #23782145 | 2 |
| C2×#19104663 | 2 |
| #23781673 | 2 |
| #23781571 | 2 |
| #23781433 | 2 |
| #339×C163 | 2 |
| #1882 | 163 |