Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. C2×C22⋊(C163⋊C8) | C2 | semidirect |
| 3. #23781390 | C2 | semidirect |
| 4. #23781388 | C2 | semidirect |
| 5. #407×C163 | C2 | semidirect |
| 111. C163 | #1468 | semidirect |
| 114. #407 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104718 | 2 |
| C2×C22⋊(C163⋊C8) | 2 |
| #23781390 | 2 |
| #23781388 | 2 |
| #407×C163 | 2 |
| #1468 | 163 |