Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
428 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 127 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. C4×Q8×D163 | C2 | semidirect |
| 3. #23781985 | C2 | semidirect |
| 4. #23781947 | C2 | semidirect |
| 5. #23781866 | C2 | semidirect |
| 6. #23781865 | C2 | semidirect |
| 7. #23781805 | C2 | semidirect |
| 8. #23781752 | C2 | semidirect |
| 9. #23781750 | C2 | semidirect |
| 10. #23781717 | C2 | semidirect |
| 11. #475×C163 | C2 | semidirect |
| 87. Dic326 | #41 | semidirect |
| 104. C4×D163 | SD16 | semidirect |
| 108. Q8×C163 | #41 | semidirect |
| 140. C163 | #3103 | semidirect |
| 146. #475 | D163 | semidirect |
| 231. Q8 | #14579700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782216 | 2 |
| C4×Q8×D163 | 2 |
| #23781985 | 2 |
| #23781947 | 2 |
| #23781866 | 2 |
| #23781865 | 2 |
| #23781805 | 2 |
| #23781752 | 2 |
| #23781750 | 2 |
| #23781717 | 2 |
| #475×C163 | 2 |
| #3103 | 163 |