Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19104763 | C2 | semidirect |
| 2. C2×#19104761 | C2 | semidirect |
| 3. C2×#19104731 | C2 | semidirect |
| 4. #23782133 | C2 | semidirect |
| 5. #23781864 | C2 | semidirect |
| 6. #23781859 | C2 | semidirect |
| 7. #23781688 | C2 | semidirect |
| 8. #23781669 | C2 | semidirect |
| 9. #418×C163 | C2 | semidirect |
| 15. C2×#14579688 | C22 | semidirect |
| 16. C2×#14579687 | C22 | semidirect |
| 17. C2×D1304 | C22 | semidirect |
| 18. C2×#14579684 | C22 | semidirect |
| 23. #19104700 | C22 | semidirect |
| 24. #19104697 | C22 | semidirect |
| 29. Dic163⋊C8 | C22 | semidirect |
| 30. #19104655 | C22 | semidirect |
| 34. #102×C163 | C22 | semidirect |
| 37. #14579699 | D4 | semidirect |
| 79. Dic326 | C2×D4 | semidirect |
| 84. D652 | C2×D4 | semidirect |
| 125. Dic163 | AGL(1,ℤ/8) | semidirect |
| 132. C163 | #3038 | semidirect |
| 142. #418 | D163 | semidirect |
| 167. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104763 | 2 |
| C2×#19104761 | 2 |
| C2×#19104731 | 2 |
| #23782133 | 2 |
| #23781864 | 2 |
| #23781859 | 2 |
| #23781688 | 2 |
| #23781669 | 2 |
| #418×C163 | 2 |
| #3038 | 163 |