Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 29. #14579683 | Q8 | semidirect |
| 45. M16×C163 | Q8 | semidirect |
| 52. C42×C163 | Q8 | semidirect |
| 95. C163 | #2061 | semidirect |
| 129. M16 | Dic326 | semidirect |
| 148. C42 | Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782293 | 2 |
| #23781708 | 2 |
| #23781707 | 2 |
| #23781531 | 2 |
| #23781433 | 2 |
| #23781425 | 2 |
| #339×C163 | 2 |
| #2061 | 163 |