Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
162 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 51 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. #23781796 | C2 | semidirect |
| 4. #23781415 | C2 | semidirect |
| 5. #23781411 | C2 | semidirect |
| 7. #462×C163 | C2 | semidirect |
| 78. C163 | #1702 | semidirect |
| 81. #462 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782013 | 2 |
| #23781865 | 2 |
| #23781796 | 2 |
| #23781415 | 2 |
| #23781411 | 2 |
| #23781408 | 2 |
| #462×C163 | 2 |
| #1702 | 163 |