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. #23782381 | C2 | semidirect |
| 2. #23782337 | C2 | semidirect |
| 3. #23782013 | C2 | semidirect |
| 4. #23781992 | C2 | semidirect |
| 5. #23781902 | C2 | semidirect |
| 6. #23781861 | C2 | semidirect |
| 7. #23781813 | C2 | semidirect |
| 8. C4×#14579686 | C2 | semidirect |
| 9. #23781730 | C2 | semidirect |
| 10. #23781660 | C2 | semidirect |
| 11. #477×C163 | C2 | semidirect |
| 132. C163 | #3305 | semidirect |
| 138. #477 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782381 | 2 |
| #23782337 | 2 |
| #23782013 | 2 |
| #23781992 | 2 |
| #23781902 | 2 |
| #23781861 | 2 |
| #23781813 | 2 |
| C4×#14579686 | 2 |
| #23781730 | 2 |
| #23781660 | 2 |
| #477×C163 | 2 |
| #3305 | 163 |