Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 8. C22×Dic326 | C4 | semidirect |
| 14. C2×C4⋊Dic163 | C4 | semidirect |
| 16. C2×Dic163⋊C4 | C4 | semidirect |
| 17. C2×Dic163⋊C4 | C4 | semidirect |
| 53. C22⋊Dic163 | Q8 | semidirect |
| 65. C22⋊C4×C163 | Q8 | semidirect |
| 145. C163 | #1996 | semidirect |
| 210. C22⋊C4 | Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104712 | 2 |
| #23781523 | 2 |
| C22⋊C4×Dic163 | 2 |
| #23781432 | 2 |
| #23781431 | 2 |
| #342×C163 | 2 |
| #1996 | 163 |