Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #23782017 | C2 | semidirect |
| 3. #23782000 | C2 | semidirect |
| 4. #23781957 | C2 | semidirect |
| 5. #23781904 | C2 | semidirect |
| 6. #23781875 | C2 | semidirect |
| 7. #23781820 | C2 | semidirect |
| 8. C4×#14579689 | C2 | semidirect |
| 10. C2×#19104658 | C2 | semidirect |
| 92. D4×C163 | Q16 | semidirect |
| 122. C163 | #3299 | semidirect |
| 208. D4 | #14579689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic326 | 2 |
| #23782017 | 2 |
| #23782000 | 2 |
| #23781957 | 2 |
| #23781904 | 2 |
| #23781875 | 2 |
| #23781820 | 2 |
| C4×#14579689 | 2 |
| D4×C163⋊C8 | 2 |
| C2×#19104658 | 2 |
| #554×C163 | 2 |
| #3299 | 163 |