Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. #23781989 | C2 | semidirect |
| 3. #23781983 | C2 | semidirect |
| 4. #23781978 | C2 | semidirect |
| 5. #23781708 | C2 | semidirect |
| 6. #23781669 | C2 | semidirect |
| 7. #23781629 | C2 | semidirect |
| 8. C2×#117×C163 | C2 | semidirect |
| 18. #19104668 | C22 | semidirect |
| 19. #19104666 | C22 | semidirect |
| 20. #19104655 | C22 | semidirect |
| 21. #19104655 | C22 | semidirect |
| 22. C22⋊(C163⋊C8) | C22 | semidirect |
| 23. C22⋊(C163⋊C8) | C22 | semidirect |
| 28. #117×C163 | C22 | semidirect |
| 29. C2×C4⋊C4×C163 | C22 | semidirect |
| 30. C2×C4⋊C4×C163 | C22 | semidirect |
| 125. C163 | #3094 | semidirect |
| 128. C2×#117 | D163 | semidirect |
| 146. #117 | C2×D163 | semidirect |
| 148. C2×C4⋊C4 | C2×D163 | semidirect |
| 149. C2×C4⋊C4 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104709 | 2 |
| #23781989 | 2 |
| #23781983 | 2 |
| #23781978 | 2 |
| #23781708 | 2 |
| #23781669 | 2 |
| #23781629 | 2 |
| C2×#117×C163 | 2 |
| #3094 | 163 |