Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782336 | C2 | semidirect |
| 3. #23782012 | C2 | semidirect |
| 4. #23781990 | C2 | semidirect |
| 5. #23781961 | C2 | semidirect |
| 6. #23781901 | C2 | semidirect |
| 7. #23781861 | C2 | semidirect |
| 8. #23781812 | C2 | semidirect |
| 9. C4×#14579688 | C2 | semidirect |
| 10. #23781662 | C2 | semidirect |
| 11. C8×D4×C163 | C2 | semidirect |
| 132. C163 | #3305 | semidirect |
| 143. C8×D4 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782380 | 2 |
| #23782336 | 2 |
| #23782012 | 2 |
| #23781990 | 2 |
| #23781961 | 2 |
| #23781901 | 2 |
| #23781861 | 2 |
| #23781812 | 2 |
| C4×#14579688 | 2 |
| #23781662 | 2 |
| C8×D4×C163 | 2 |
| #3305 | 163 |