Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 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. C2×#19104694 | C2 | semidirect |
| 3. #23781605 | C2 | semidirect |
| 4. #23781602 | C2 | semidirect |
| 5. #23781597 | C2 | semidirect |
| 6. #23781592 | C2 | semidirect |
| 7. #23781590 | C2 | semidirect |
| 9. C4×C4⋊Dic163 | C2 | semidirect |
| 10. C4×(C2×D163)⋊C4 | C2 | semidirect |
| 11. C4×C22⋊C4×C163 | C2 | semidirect |
| 137. C163 | #2395 | semidirect |
| 149. C4×C22⋊C4 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D163 | 2 |
| C2×#19104694 | 2 |
| #23781605 | 2 |
| #23781602 | 2 |
| #23781597 | 2 |
| #23781592 | 2 |
| #23781590 | 2 |
| #23781581 | 2 |
| C4×C4⋊Dic163 | 2 |
| C4×(C2×D163)⋊C4 | 2 |
| C4×C22⋊C4×C163 | 2 |
| #2395 | 163 |