Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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×#19104742 | C2 | semidirect |
| 2. #23782148 | C2 | semidirect |
| 3. #23781670 | C2 | semidirect |
| 4. #23781666 | C2 | semidirect |
| 5. #23781661 | C2 | semidirect |
| 6. C2×#19104656 | C2 | semidirect |
| 9. C2×#14579683 | C22 | semidirect |
| 10. C22×C163⋊C8 | C22 | semidirect |
| 13. #19104694 | C22 | semidirect |
| 14. C2×C4⋊Dic163 | C22 | semidirect |
| 15. #19104659 | C22 | semidirect |
| 16. #19104659 | C22 | semidirect |
| 17. #19104656 | C22 | semidirect |
| 18. #19104656 | C22 | semidirect |
| 19. #19104656 | C22 | semidirect |
| 21. H(5,𝔽2)×C163 | C4 | semidirect |
| 41. #41×C163 | C2×C4 | semidirect |
| 49. C2×D4×C163 | C2×C4 | semidirect |
| 97. C163 | #2897 | semidirect |
| 107. H(5,𝔽2) | Dic163 | semidirect |
| 129. #41 | C2×Dic163 | semidirect |
| 137. C2×D4 | C2×Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104742 | 2 |
| #23782148 | 2 |
| #23781670 | 2 |
| #23781666 | 2 |
| #23781661 | 2 |
| C2×#19104656 | 2 |
| C2×H(5,𝔽2)×C163 | 2 |
| #2897 | 163 |