Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23782277 | C2 | semidirect |
| 3. #23782007 | C2 | semidirect |
| 4. #23781966 | C2 | semidirect |
| 5. #23781871 | C2 | semidirect |
| 7. #23781767 | C2 | semidirect |
| 8. C4×#14579688 | C2 | semidirect |
| 9. #433×C163 | C2 | semidirect |
| 13. #19104735 | C22 | semidirect |
| 15. #19104727 | C22 | semidirect |
| 18. C4×Dic326 | C22 | semidirect |
| 24. #19104669 | C22 | semidirect |
| 25. #19104667 | C22 | semidirect |
| 26. #19104660 | C22 | semidirect |
| 27. #19104660 | C22 | semidirect |
| 31. C4⋊C8×C163 | C22 | semidirect |
| 33. #97×C163 | C22 | semidirect |
| 34. C4×C8×C163 | C22 | semidirect |
| 102. C163 | #3123 | semidirect |
| 112. #433 | D163 | semidirect |
| 130. C4⋊C8 | C2×D163 | semidirect |
| 136. #97 | C2×D163 | semidirect |
| 137. C4×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782277 | 2 |
| #23782139 | 2 |
| #23782007 | 2 |
| #23781966 | 2 |
| #23781871 | 2 |
| #23781818 | 2 |
| #23781767 | 2 |
| C4×#14579688 | 2 |
| #433×C163 | 2 |
| #3123 | 163 |