Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 1. #23782293 | C2 | semidirect |
| 3. #23782030 | C2 | semidirect |
| 4. #23782025 | C2 | semidirect |
| 5. #23782020 | C2 | semidirect |
| 6. #23782012 | C2 | semidirect |
| 7. #23781671 | C2 | semidirect |
| 8. #23781667 | C2 | semidirect |
| 9. #23781662 | C2 | semidirect |
| 10. C2×#19104657 | C2 | semidirect |
| 11. #405×C163 | C2 | semidirect |
| 14. #19104735 | C22 | semidirect |
| 17. #19104727 | C22 | semidirect |
| 26. #19104660 | C22 | semidirect |
| 27. #19104660 | C22 | semidirect |
| 28. #19104660 | C22 | semidirect |
| 33. #19104657 | C22 | semidirect |
| 34. #19104657 | C22 | semidirect |
| 35. #19104657 | C22 | semidirect |
| 39. #97×C163 | C22 | semidirect |
| 40. C4×C8×C163 | C22 | semidirect |
| 135. C163 | #3136 | semidirect |
| 147. #405 | D163 | semidirect |
| 175. #97 | C2×D163 | semidirect |
| 176. C4×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782293 | 2 |
| #23782234 | 2 |
| #23782030 | 2 |
| #23782025 | 2 |
| #23782020 | 2 |
| #23782012 | 2 |
| #23781671 | 2 |
| #23781667 | 2 |
| #23781662 | 2 |
| C2×#19104657 | 2 |
| #405×C163 | 2 |
| #3136 | 163 |