Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19104692 | C2 | semidirect |
| 3. C2×#19104663 | C2 | semidirect |
| 4. C2×#19104661 | C2 | semidirect |
| 5. #23781628 | C2 | semidirect |
| 6. #23781424 | C2 | semidirect |
| 7. #339×C163 | C2 | semidirect |
| 12. #19104715 | C4 | semidirect |
| 13. #19104710 | C4 | semidirect |
| 54. C4×Dic163 | D4 | semidirect |
| 64. C42×C163 | D4 | semidirect |
| 127. C163 | #1897 | semidirect |
| 135. #339 | D163 | semidirect |
| 192. C42 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782177 | 2 |
| C2×#19104692 | 2 |
| C2×#19104663 | 2 |
| C2×#19104661 | 2 |
| #23781628 | 2 |
| #23781424 | 2 |
| #339×C163 | 2 |
| #1897 | 163 |