Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19104700 | C2 | semidirect |
| 3. #23781983 | C2 | semidirect |
| 4. #23781949 | C2 | semidirect |
| 5. #23781864 | C2 | semidirect |
| 6. #23781806 | C2 | semidirect |
| 7. #23781803 | C2 | semidirect |
| 8. #23781756 | C2 | semidirect |
| 9. #23781752 | C2 | semidirect |
| 10. #23781715 | C2 | semidirect |
| 11. #481×C163 | C2 | semidirect |
| 86. Dic326 | #41 | semidirect |
| 96. C2×Dic163 | SD16 | semidirect |
| 140. C163 | #3103 | semidirect |
| 145. #481 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782210 | 2 |
| C2×#19104700 | 2 |
| #23781983 | 2 |
| #23781949 | 2 |
| #23781864 | 2 |
| #23781806 | 2 |
| #23781803 | 2 |
| #23781756 | 2 |
| #23781752 | 2 |
| #23781715 | 2 |
| #481×C163 | 2 |
| #3103 | 163 |