Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 1. #23782286 | C2 | semidirect |
| 2. #23782063 | C2 | semidirect |
| 3. #23782049 | C2 | semidirect |
| 4. #23782025 | C2 | semidirect |
| 5. #23781923 | C2 | semidirect |
| 7. #23781894 | C2 | semidirect |
| 8. #23781778 | C2 | semidirect |
| 9. #23781773 | C2 | semidirect |
| 10. C4×#14579688 | C2 | semidirect |
| 11. #405×C163 | C2 | semidirect |
| 109. C163 | #3173 | semidirect |
| 121. #405 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782286 | 2 |
| #23782063 | 2 |
| #23782049 | 2 |
| #23782025 | 2 |
| #23781923 | 2 |
| #23781918 | 2 |
| #23781894 | 2 |
| #23781778 | 2 |
| #23781773 | 2 |
| C4×#14579688 | 2 |
| #405×C163 | 2 |
| #3173 | 163 |