Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
416 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 173 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. #23781951 | C2 | direct (N × H) |
| 27. C2×Dic326 | Q8 | semidirect |
| 49. Dic326 | C2×Q8 | semidirect |
| 78. C2×C163 | #475 | semidirect |
| 82. C163 | C2×#475 | semidirect |
| 161. C2 | #23781951 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104735 | 2 |
| C2×C4×Dic326 | 2 |
| #23781951 | 2 |
| C2×#19104667 | 2 |
| C2×#19104660 | 2 |
| C2×C4⋊C8×C163 | 2 |
| C2×#475 | 163 |