Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
994 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 173 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×#19104761 | C2 | semidirect |
| 2. #23782176 | C2 | semidirect |
| 3. #23781816 | C2 | semidirect |
| 4. #23781799 | C2 | semidirect |
| 5. #23781670 | C2 | semidirect |
| 6. #23781629 | C2 | semidirect |
| 7. C23×D4×C163 | C2 | semidirect |
| 8. C2×#14579699 | C22 | semidirect |
| 10. C2×#14579687 | C22 | semidirect |
| 11. C2×#14579684 | C22 | semidirect |
| 12. C2×#14579683 | C22 | semidirect |
| 14. #19104714 | C22 | semidirect |
| 15. #19104709 | C22 | semidirect |
| 18. #19104694 | C22 | semidirect |
| 19. #19104656 | C22 | semidirect |
| 20. C22⋊(C163⋊C8) | C22 | semidirect |
| 29. C2×Dic326 | C23 | semidirect |
| 30. C2×D652 | C23 | semidirect |
| 37. C2×C163⋊C8 | C23 | semidirect |
| 38. C4⋊Dic163 | C23 | semidirect |
| 55. C2×D4×C163 | D4 | semidirect |
| 102. C22×C163 | AGL(1,ℤ/8) | semidirect |
| 117. C163 | #3003 | semidirect |
| 119. C23×D4 | D163 | semidirect |
| 162. C2×D4 | C22⋊D163 | semidirect |
| 222. C22 | #19104761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| #23782176 | 2 |
| #23781816 | 2 |
| #23781799 | 2 |
| #23781670 | 2 |
| #23781629 | 2 |
| C23×D4×C163 | 2 |
| #3003 | 163 |