Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
520 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 185 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×#19104743 | C2 | semidirect |
| 2. C22×C8×D163 | C2 | semidirect |
| 4. #23781735 | C2 | semidirect |
| 5. #23781730 | C2 | semidirect |
| 6. #23781631 | C2 | semidirect |
| 7. #23781628 | C2 | semidirect |
| 8. #23781621 | C2 | semidirect |
| 9. #424×C163 | C2 | semidirect |
| 14. C2×#14579682 | C22 | semidirect |
| 19. C2×C8×D163 | C22 | semidirect |
| 26. (C2×D163)⋊C8 | C22 | semidirect |
| 27. #19104646 | C22 | semidirect |
| 28. C4×C163⋊C8 | C22 | semidirect |
| 32. C4⋊C8×C163 | C22 | semidirect |
| 48. C2×C163⋊C8 | D4 | semidirect |
| 101. C2×D163 | #131 | semidirect |
| 113. C163 | #2929 | semidirect |
| 120. #424 | D163 | semidirect |
| 142. C4⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104743 | 2 |
| C22×C8×D163 | 2 |
| #23782177 | 2 |
| #23781735 | 2 |
| #23781730 | 2 |
| #23781631 | 2 |
| #23781628 | 2 |
| #23781621 | 2 |
| #424×C163 | 2 |
| #2929 | 163 |