Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19104781 | C2 | semidirect |
| 2. C2×#19104760 | C2 | semidirect |
| 3. C22×D1304 | C2 | semidirect |
| 4. #23782234 | C2 | semidirect |
| 5. #23781813 | C2 | semidirect |
| 6. #23781800 | C2 | semidirect |
| 7. #23781669 | C2 | semidirect |
| 8. #23781631 | C2 | semidirect |
| 9. #416×C163 | C2 | semidirect |
| 12. C2×#14579700 | C22 | semidirect |
| 17. C22×D652 | C22 | semidirect |
| 19. C2×D4×D163 | C22 | semidirect |
| 21. C2×#14579686 | C22 | semidirect |
| 23. C2×D1304 | C22 | semidirect |
| 24. C2×#14579684 | C22 | semidirect |
| 25. C2×#14579683 | C22 | semidirect |
| 28. #19104710 | C22 | semidirect |
| 30. #19104655 | C22 | semidirect |
| 31. (C2×D163)⋊C8 | C22 | semidirect |
| 33. C22×C8×C163 | C22 | semidirect |
| 34. #117×C163 | C22 | semidirect |
| 35. #103×C163 | C22 | semidirect |
| 36. #102×C163 | C22 | semidirect |
| 55. C2×D652 | D4 | semidirect |
| 72. #41×C163 | D4 | semidirect |
| 151. C163 | #3008 | semidirect |
| 160. #416 | D163 | semidirect |
| 179. C22×C8 | C2×D163 | semidirect |
| 184. #117 | C2×D163 | semidirect |
| 185. #103 | C2×D163 | semidirect |
| 187. #102 | C2×D163 | semidirect |
| 198. #41 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104781 | 2 |
| C2×#19104760 | 2 |
| C22×D1304 | 2 |
| #23782234 | 2 |
| #23781813 | 2 |
| #23781800 | 2 |
| #23781669 | 2 |
| #23781631 | 2 |
| #416×C163 | 2 |
| #3008 | 163 |