Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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 |
| 3. C2×#19104723 | C2 | semidirect |
| 4. C4×#14579699 | C2 | semidirect |
| 5. #23781888 | C2 | semidirect |
| 6. #23781881 | C2 | semidirect |
| 7. #23781675 | C2 | semidirect |
| 8. #23781671 | C2 | semidirect |
| 9. #423×C163 | C2 | semidirect |
| 15. C2×Dic652 | C22 | semidirect |
| 17. C2×#14579688 | C22 | semidirect |
| 22. C4×Dic326 | C22 | semidirect |
| 23. C4×D652 | C22 | semidirect |
| 29. #19104660 | C22 | semidirect |
| 34. C4⋊C8×C163 | C22 | semidirect |
| 125. C163 | #3040 | semidirect |
| 133. #423 | D163 | semidirect |
| 158. 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 |
| C2×#19104763 | 2 |
| C2×#19104723 | 2 |
| C4×#14579699 | 2 |
| #23781888 | 2 |
| #23781881 | 2 |
| #23781675 | 2 |
| #23781671 | 2 |
| #423×C163 | 2 |
| #3040 | 163 |