Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #23782380 | C2 | semidirect |
| 2. #23782337 | C2 | semidirect |
| 3. #23782012 | C2 | semidirect |
| 4. #23781991 | C2 | semidirect |
| 5. #23781960 | C2 | semidirect |
| 6. #23781900 | C2 | semidirect |
| 7. #23781860 | C2 | semidirect |
| 8. #23781809 | C2 | semidirect |
| 9. C8×D652 | C2 | semidirect |
| 10. #23781660 | C2 | semidirect |
| 11. C4×SD16×C163 | C2 | semidirect |
| 132. C163 | #3305 | semidirect |
| 142. C4×SD16 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782380 | 2 |
| #23782337 | 2 |
| #23782012 | 2 |
| #23781991 | 2 |
| #23781960 | 2 |
| #23781900 | 2 |
| #23781860 | 2 |
| #23781809 | 2 |
| C8×D652 | 2 |
| #23781660 | 2 |
| C4×SD16×C163 | 2 |
| #3305 | 163 |