Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
166 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 49 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. #23782043 | C2 | semidirect |
| 5. Dic163⋊C16 | C2 | semidirect |
| 6. #23781468 | C2 | semidirect |
| 7. #358×C163 | C2 | semidirect |
| 68. Dic163 | SD32 | semidirect |
| 73. C163 | #2208 | semidirect |
| 81. #358 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104680 | 2 |
| C2×#19104678 | 2 |
| #23782043 | 2 |
| #23781747 | 2 |
| Dic163⋊C16 | 2 |
| #23781468 | 2 |
| #358×C163 | 2 |
| #2208 | 163 |