Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#19104782 | C2 | semidirect |
| 2. C2×#19104763 | C2 | semidirect |
| 3. C22×#14579688 | C2 | semidirect |
| 4. #23782229 | C2 | semidirect |
| 5. #23781812 | C2 | semidirect |
| 6. #23781806 | C2 | semidirect |
| 7. #23781675 | C2 | semidirect |
| 8. #23781662 | C2 | semidirect |
| 9. #408×C163 | C2 | semidirect |
| 13. C2×#14579699 | C22 | semidirect |
| 17. C22×Dic326 | C22 | semidirect |
| 30. #19104660 | C22 | semidirect |
| 31. #19104660 | C22 | semidirect |
| 32. #19104657 | C22 | semidirect |
| 36. C22⋊C8×C163 | C22 | semidirect |
| 41. #14579699 | D4 | semidirect |
| 49. C2×Dic326 | D4 | semidirect |
| 145. C163 | #3010 | semidirect |
| 155. #408 | D163 | semidirect |
| 182. C22⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104782 | 2 |
| C2×#19104763 | 2 |
| C22×#14579688 | 2 |
| #23782229 | 2 |
| #23781812 | 2 |
| #23781806 | 2 |
| #23781675 | 2 |
| #23781662 | 2 |
| #408×C163 | 2 |
| #3010 | 163 |