Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. C22×#14579688 | C2 | semidirect |
| 3. #23782241 | C2 | semidirect |
| 4. #23782139 | C2 | semidirect |
| 5. #23781881 | C2 | semidirect |
| 6. #23781871 | C2 | semidirect |
| 7. #23781675 | C2 | semidirect |
| 8. #23781662 | C2 | semidirect |
| 9. #424×C163 | C2 | semidirect |
| 18. #19104735 | C22 | semidirect |
| 19. #19104723 | C22 | semidirect |
| 26. #19104660 | C22 | semidirect |
| 27. #19104660 | C22 | semidirect |
| 28. #19104657 | C22 | semidirect |
| 32. C4⋊C8×C163 | C22 | semidirect |
| 116. C163 | #3042 | semidirect |
| 124. #424 | D163 | semidirect |
| 146. C4⋊C8 | 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×#14579688 | 2 |
| #23782241 | 2 |
| #23782139 | 2 |
| #23781881 | 2 |
| #23781871 | 2 |
| #23781675 | 2 |
| #23781662 | 2 |
| #424×C163 | 2 |
| #3042 | 163 |