Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
752 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#14579687 | C2 | semidirect |
| 3. #23782236 | C2 | semidirect |
| 4. #23781827 | C2 | semidirect |
| 5. #23781816 | C2 | semidirect |
| 6. #23781670 | C2 | semidirect |
| 7. #23781661 | C2 | semidirect |
| 8. #23781632 | C2 | semidirect |
| 10. C22×Dic326 | C22 | semidirect |
| 12. C2×#14579689 | C22 | semidirect |
| 14. C2×#14579687 | C22 | semidirect |
| 15. C2×#14579687 | C22 | semidirect |
| 16. C2×#14579683 | C22 | semidirect |
| 17. C22×C163⋊C8 | C22 | semidirect |
| 21. #19104714 | C22 | semidirect |
| 22. #19104694 | C22 | semidirect |
| 23. #19104659 | C22 | semidirect |
| 24. #19104656 | C22 | semidirect |
| 25. #19104656 | C22 | semidirect |
| 26. C22⋊(C163⋊C8) | C22 | semidirect |
| 146. C163 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C22×#14579687 | 2 |
| #23782236 | 2 |
| #23781827 | 2 |
| #23781816 | 2 |
| #23781670 | 2 |
| #23781661 | 2 |
| #23781632 | 2 |
| C2×H(5,𝔽2)×C163 | 2 |
| #3009 | 163 |