Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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. #23781906 | C2 | semidirect |
| 4. #23781901 | C2 | semidirect |
| 5. #23781894 | C2 | semidirect |
| 6. #23781703 | C2 | semidirect |
| 7. #23781662 | C2 | semidirect |
| 8. C23×C8×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 |
| 91. C22×C163 | #135 | semidirect |
| 106. C163 | #3050 | semidirect |
| 109. C23×C8 | D163 | semidirect |
| 157. C2×C8 | C22⋊D163 | semidirect |
| 200. C22 | #19104757 | 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 |
| #23781906 | 2 |
| #23781901 | 2 |
| #23781894 | 2 |
| #23781703 | 2 |
| #23781662 | 2 |
| C23×C8×C163 | 2 |
| #3050 | 163 |