Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23781962 | C2 | semidirect |
| 3. #23781962 | C2 | semidirect |
| 4. #23781952 | C2 | semidirect |
| 5. #23781942 | C2 | semidirect |
| 6. #23781705 | C2 | semidirect |
| 7. #23781701 | C2 | semidirect |
| 8. #23781692 | C2 | semidirect |
| 11. #544×C163 | C2 | semidirect |
| 21. #19104668 | C22 | semidirect |
| 22. #19104668 | C22 | semidirect |
| 23. #19104668 | C22 | semidirect |
| 24. #19104666 | C22 | semidirect |
| 25. #19104666 | C22 | semidirect |
| 26. #19104666 | C22 | semidirect |
| 27. C4⋊(C163⋊C8) | C22 | semidirect |
| 28. C4⋊(C163⋊C8) | C22 | semidirect |
| 34. C4⋊Q8×C163 | C22 | semidirect |
| 36. #125×C163 | C22 | semidirect |
| 44. C2×D652 | Q8 | semidirect |
| 124. C163 | #3081 | semidirect |
| 126. #544 | D163 | semidirect |
| 141. C4⋊Q8 | C2×D163 | semidirect |
| 143. #125 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782139 | 2 |
| #23781962 | 2 |
| #23781952 | 2 |
| #23781942 | 2 |
| #23781705 | 2 |
| #23781701 | 2 |
| #23781692 | 2 |
| #23781669 | 2 |
| C2×#19104655 | 2 |
| #544×C163 | 2 |
| #3081 | 163 |