Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23782073 | C2 | semidirect |
| 4. #23782072 | C2 | semidirect |
| 5. #23782066 | C2 | semidirect |
| 6. #23782062 | C2 | semidirect |
| 44. C2×C163⋊C8 | Q8 | semidirect |
| 65. M16×C163 | Q8 | semidirect |
| 112. C163 | #3163 | semidirect |
| 159. M16 | Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782296 | 2 |
| #23782293 | 2 |
| #23782073 | 2 |
| #23782072 | 2 |
| #23782066 | 2 |
| #23782062 | 2 |
| #23781707 | 2 |
| #23781701 | 2 |
| C2×#19104666 | 2 |
| #23781623 | 2 |
| #428×C163 | 2 |
| #3163 | 163 |