Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19104765 | C2 | semidirect |
| 2. C2×#19104761 | C2 | semidirect |
| 3. C2×#19104755 | C2 | semidirect |
| 4. C22×#14579687 | C2 | semidirect |
| 5. #23782241 | C2 | semidirect |
| 6. #23782060 | C2 | semidirect |
| 7. #23782052 | C2 | semidirect |
| 8. #23782047 | C2 | semidirect |
| 9. #23782037 | C2 | semidirect |
| 10. #23781621 | C2 | semidirect |
| 11. #535×C163 | C2 | semidirect |
| 17. C2×#14579689 | C22 | semidirect |
| 18. C2×#14579689 | C22 | semidirect |
| 23. C2×#14579687 | C22 | semidirect |
| 24. C2×#14579687 | C22 | semidirect |
| 25. C2×#14579686 | C22 | semidirect |
| 27. C2×#14579684 | C22 | semidirect |
| 30. #19104735 | C22 | semidirect |
| 31. #19104723 | C22 | semidirect |
| 34. #19104646 | C22 | semidirect |
| 35. C4×C163⋊C8 | C22 | semidirect |
| 64. #14579683 | D4 | semidirect |
| 65. C2×C163⋊C8 | D4 | semidirect |
| 148. C163 | #3154 | semidirect |
| 155. #535 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C2×#19104761 | 2 |
| C2×#19104755 | 2 |
| C22×#14579687 | 2 |
| #23782241 | 2 |
| #23782060 | 2 |
| #23782052 | 2 |
| #23782047 | 2 |
| #23782037 | 2 |
| #23781621 | 2 |
| #535×C163 | 2 |
| #3154 | 163 |