Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
584 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19104760 | C2 | semidirect |
| 2. C2×#19104731 | C2 | semidirect |
| 3. #41×Dic163 | C2 | semidirect |
| 4. #23781863 | C2 | semidirect |
| 5. #23781858 | C2 | semidirect |
| 6. #23781688 | C2 | semidirect |
| 7. #23781671 | C2 | semidirect |
| 8. #23781670 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C163 | C2 | semidirect |
| 13. C2×#14579686 | C22 | semidirect |
| 14. C2×#14579684 | C22 | semidirect |
| 19. Q8×Dic163 | C22 | semidirect |
| 21. D4×Dic163 | C22 | semidirect |
| 26. Dic163⋊C8 | C22 | semidirect |
| 27. #19104657 | C22 | semidirect |
| 28. #19104656 | C22 | semidirect |
| 32. C2×SD16×C163 | C22 | semidirect |
| 33. C2×D8×C163 | C22 | semidirect |
| 60. #41×C163 | D4 | semidirect |
| 94. Q8×C163 | C2×D4 | semidirect |
| 100. D4×C163 | C2×D4 | semidirect |
| 125. Dic163 | AGL(1,ℤ/8) | semidirect |
| 132. C163 | #3038 | semidirect |
| 135. C2×AGL(1,ℤ/8) | D163 | semidirect |
| 150. C2×SD16 | C2×D163 | semidirect |
| 152. C2×D8 | C2×D163 | semidirect |
| 171. #41 | C22⋊D163 | semidirect |
| 216. Q8 | C2×C22⋊D163 | semidirect |
| 227. D4 | C2×C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104760 | 2 |
| C2×#19104731 | 2 |
| #41×Dic163 | 2 |
| #23781863 | 2 |
| #23781858 | 2 |
| #23781688 | 2 |
| #23781671 | 2 |
| #23781670 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #3038 | 163 |