Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19104757 | C2 | semidirect |
| 2. #23782176 | C2 | semidirect |
| 3. #23781923 | C2 | semidirect |
| 4. #23781918 | C2 | semidirect |
| 5. #23781911 | C2 | semidirect |
| 6. #23781703 | C2 | semidirect |
| 7. #23781662 | C2 | semidirect |
| 8. C22×M16×C163 | C2 | semidirect |
| 11. C2×Dic652 | C22 | semidirect |
| 12. C2×#14579688 | C22 | semidirect |
| 13. C2×D1304 | C22 | semidirect |
| 20. #19104669 | C22 | semidirect |
| 21. #19104667 | C22 | semidirect |
| 22. #19104660 | C22 | semidirect |
| 23. #19104657 | C22 | semidirect |
| 56. C2×C8×C163 | D4 | semidirect |
| 105. C163 | #3054 | semidirect |
| 108. C22×M16 | D163 | semidirect |
| 156. C2×C8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104757 | 2 |
| #23782176 | 2 |
| #23781923 | 2 |
| #23781918 | 2 |
| #23781911 | 2 |
| #23781703 | 2 |
| #23781662 | 2 |
| C22×M16×C163 | 2 |
| #3054 | 163 |