Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 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×#19104782 | C2 | semidirect |
| 2. #23782480 | C2 | semidirect |
| 3. #23782476 | C2 | semidirect |
| 4. #23782463 | C2 | semidirect |
| 5. C2×#19104765 | C2 | semidirect |
| 6. #23782432 | C2 | semidirect |
| 7. #585×C163 | C2 | semidirect |
| 9. #19104782 | C22 | semidirect |
| 10. C2×#14579699 | C22 | semidirect |
| 12. C22×Dic326 | C22 | semidirect |
| 14. #19104766 | C22 | semidirect |
| 15. #19104765 | C22 | semidirect |
| 16. #19104765 | C22 | semidirect |
| 17. #19104761 | C22 | semidirect |
| 18. #19104760 | C22 | semidirect |
| 19. #19104755 | C22 | semidirect |
| 20. C2×#14579689 | C22 | semidirect |
| 21. C2×#14579687 | C22 | semidirect |
| 22. #19104742 | C22 | semidirect |
| 23. C2×#14579683 | C22 | semidirect |
| 25. 2−1+4×C163 | C22 | semidirect |
| 27. H(5,𝔽2)×C163 | C22 | semidirect |
| 112. C163 | #3586 | semidirect |
| 114. #585 | D163 | semidirect |
| 124. 2−1+4 | C2×D163 | semidirect |
| 126. H(5,𝔽2) | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104782 | 2 |
| #23782480 | 2 |
| #23782476 | 2 |
| #23782463 | 2 |
| C2×#19104765 | 2 |
| #23782432 | 2 |
| #585×C163 | 2 |
| #3586 | 163 |