Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
800 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
|---|---|---|
| 2. #23782139 | C2 | semidirect |
| 3. #23781639 | C2 | semidirect |
| 4. #23781638 | C2 | semidirect |
| 5. #99×D163 | C2 | semidirect |
| 6. #410×C163 | C2 | semidirect |
| 9. C2×#14579700 | C4 | semidirect |
| 10. C2×#14579699 | C4 | semidirect |
| 12. C22×D652 | C4 | semidirect |
| 14. C2×D4×D163 | C4 | semidirect |
| 18. #19104694 | C22 | semidirect |
| 19. C22⋊C4×D163 | C22 | semidirect |
| 20. #19104650 | C22 | semidirect |
| 21. #19104649 | C22 | semidirect |
| 23. #117×C163 | C22 | semidirect |
| 24. #99×C163 | C22 | semidirect |
| 25. C23×D163 | C2×C4 | semidirect |
| 32. C2×Dic326 | C2×C4 | semidirect |
| 37. C2×D652 | C2×C4 | semidirect |
| 38. C2×D652 | C2×C4 | semidirect |
| 41. C2×C22⋊D163 | C2×C4 | semidirect |
| 46. C2×C4×D163 | C2×C4 | semidirect |
| 47. C2×C4×D163 | C2×C4 | semidirect |
| 54. C2×Q8×C163 | C2×C4 | semidirect |
| 55. C2×D4×C163 | C2×C4 | semidirect |
| 57. C22×C4×C163 | C2×C4 | semidirect |
| 120. C163 | #2883 | semidirect |
| 126. #410 | D163 | semidirect |
| 141. #117 | C2×D163 | semidirect |
| 145. #99 | C2×D163 | semidirect |
| 156. C2×Q8 | C4×D163 | semidirect |
| 169. C2×D4 | C4×D163 | semidirect |
| 174. C22×C4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104781 | 2 |
| #23782139 | 2 |
| #23781639 | 2 |
| #23781638 | 2 |
| #99×D163 | 2 |
| #410×C163 | 2 |
| #2883 | 163 |