Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 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×#19104765 | C2 | semidirect |
| 3. C22×#14579688 | C2 | semidirect |
| 4. #23781928 | C2 | direct (N × H) |
| 5. C2×#19104671 | C2 | semidirect |
| 6. C2×#19104653 | C2 | semidirect |
| 7. C2×#19104651 | C2 | semidirect |
| 8. C2×#131×C163 | C2 | semidirect |
| 12. #19104765 | C22 | semidirect |
| 19. C2×#14579688 | C22 | semidirect |
| 25. #19104671 | C22 | semidirect |
| 26. #19104653 | C22 | semidirect |
| 27. #19104651 | C22 | semidirect |
| 30. #131×C163 | C22 | semidirect |
| 135. C2×C163 | #471 | semidirect |
| 138. C163 | C2×#471 | semidirect |
| 143. C2×#131 | D163 | semidirect |
| 164. #131 | C2×D163 | semidirect |
| 275. C2 | #23781928 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C2×#19104760 | 2 |
| C22×#14579688 | 2 |
| #23781928 | 2 |
| C2×#19104671 | 2 |
| C2×#19104653 | 2 |
| C2×#19104651 | 2 |
| C2×#131×C163 | 2 |
| C2×#471 | 163 |