Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
156 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23781492 | C2 | semidirect |
| 4. #23781490 | C2 | semidirect |
| 7. #19104675 | C4 | semidirect |
| 20. C163⋊C16 | C2×C4 | semidirect |
| 55. C163 | #2159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104675 | 2 |
| #23781703 | 2 |
| #23781492 | 2 |
| #23781490 | 2 |
| C2×#107×C163 | 2 |
| #2159 | 163 |