Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 9. #19104734 | C4 | semidirect |
| 10. #19104734 | C4 | semidirect |
| 11. #19104726 | C4 | semidirect |
| 12. #19104726 | C4 | semidirect |
| 33. #14579683 | Q8 | semidirect |
| 55. M16×C163 | Q8 | semidirect |
| 114. C163 | #1986 | semidirect |
| 152. M16 | Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782218 | 2 |
| M16×Dic163 | 2 |
| C4×Dic163⋊C4 | 2 |
| #23781426 | 2 |
| #23781425 | 2 |
| #23781424 | 2 |
| #339×C163 | 2 |
| #1986 | 163 |