Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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×C4×D652 | C2 | semidirect |
| 2. #23781976 | C2 | semidirect |
| 3. #23781942 | C2 | semidirect |
| 4. #23781857 | C2 | semidirect |
| 5. #23781798 | C2 | semidirect |
| 6. C4×#14579684 | C2 | semidirect |
| 7. #23781718 | C2 | semidirect |
| 8. #532×C163 | C2 | semidirect |
| 18. #19104668 | C22 | semidirect |
| 19. C4⋊(C163⋊C8) | C22 | semidirect |
| 20. #19104656 | C22 | semidirect |
| 23. C4×C163⋊C8 | C22 | semidirect |
| 25. C4⋊Q8×C163 | C22 | semidirect |
| 26. #127×C163 | C22 | semidirect |
| 31. C4×D4×C163 | C22 | semidirect |
| 71. D652 | #41 | semidirect |
| 88. C2×C4×C163 | D8 | semidirect |
| 120. C163 | #3100 | semidirect |
| 122. #532 | D163 | semidirect |
| 134. C4⋊Q8 | C2×D163 | semidirect |
| 135. #127 | C2×D163 | semidirect |
| 144. C4×D4 | C2×D163 | semidirect |
| 208. C2×C4 | #14579684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D652 | 2 |
| #23781976 | 2 |
| #23781942 | 2 |
| #23781857 | 2 |
| #23781798 | 2 |
| C4×#14579684 | 2 |
| #23781718 | 2 |
| #532×C163 | 2 |
| #3100 | 163 |