Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#14579686 | C2 | semidirect |
| 3. #23782239 | C2 | semidirect |
| 4. #23782139 | C2 | semidirect |
| 5. #23781883 | C2 | semidirect |
| 6. #23781869 | C2 | semidirect |
| 7. #23781693 | C2 | semidirect |
| 8. #23781659 | C2 | semidirect |
| 9. #419×C163 | C2 | semidirect |
| 18. #19104733 | C22 | semidirect |
| 19. #19104724 | C22 | semidirect |
| 26. Dic163⋊C8 | C22 | semidirect |
| 27. #19104658 | C22 | semidirect |
| 28. #19104655 | C22 | semidirect |
| 32. #103×C163 | C22 | semidirect |
| 116. C163 | #3042 | semidirect |
| 125. #419 | D163 | semidirect |
| 148. #103 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104763 | 2 |
| C22×#14579686 | 2 |
| #23782239 | 2 |
| #23782139 | 2 |
| #23781883 | 2 |
| #23781869 | 2 |
| #23781693 | 2 |
| #23781659 | 2 |
| #419×C163 | 2 |
| #3042 | 163 |