Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
206 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 51. Dic326 | Q16 | semidirect |
| 59. Q8×C163 | Q16 | semidirect |
| 82. C163 | #1633 | semidirect |
| 137. Q8 | #14579689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic326 | 2 |
| #23782044 | 2 |
| #23781957 | 2 |
| #23781413 | 2 |
| Q8⋊(C163⋊C8) | 2 |
| #23781395 | 2 |
| #477×C163 | 2 |
| #1633 | 163 |