Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 1. C2×#19104768 | C2 | semidirect |
| 2. C22×#14579688 | C2 | semidirect |
| 4. #23782142 | C2 | semidirect |
| 5. #23781888 | C2 | semidirect |
| 6. #23781866 | C2 | semidirect |
| 7. #23781671 | C2 | semidirect |
| 8. #23781662 | C2 | semidirect |
| 9. #424×C163 | C2 | semidirect |
| 14. C2×Dic652 | C22 | semidirect |
| 17. C2×#14579688 | C22 | semidirect |
| 22. C4×Dic326 | C22 | semidirect |
| 26. #19104660 | C22 | semidirect |
| 28. #19104657 | C22 | semidirect |
| 32. C4⋊C8×C163 | C22 | semidirect |
| 38. C2×Dic326 | D4 | semidirect |
| 116. C163 | #3043 | 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×#19104768 | 2 |
| C22×#14579688 | 2 |
| #23782234 | 2 |
| #23782142 | 2 |
| #23781888 | 2 |
| #23781866 | 2 |
| #23781671 | 2 |
| #23781662 | 2 |
| #424×C163 | 2 |
| #3043 | 163 |