Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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×#19104763 | C2 | semidirect |
| 2. C2×#19104755 | C2 | semidirect |
| 3. C22×#14579684 | C2 | semidirect |
| 4. #23782232 | C2 | semidirect |
| 5. #23782229 | C2 | semidirect |
| 6. #23782053 | C2 | semidirect |
| 7. #23782051 | C2 | semidirect |
| 8. #23782046 | C2 | semidirect |
| 9. #23782040 | C2 | semidirect |
| 10. #23781623 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C163 | C2 | semidirect |
| 16. C2×#14579689 | C22 | semidirect |
| 17. C2×#14579688 | C22 | semidirect |
| 18. C2×#14579687 | C22 | semidirect |
| 19. C2×#14579686 | C22 | semidirect |
| 20. C2×D1304 | C22 | semidirect |
| 24. C2×#14579684 | C22 | semidirect |
| 26. #19104731 | C22 | semidirect |
| 27. #19104731 | C22 | semidirect |
| 28. #19104724 | C22 | semidirect |
| 29. #19104722 | C22 | semidirect |
| 35. #19104645 | C22 | semidirect |
| 36. C8×Dic163 | C22 | semidirect |
| 40. C2×SD16×C163 | C22 | semidirect |
| 41. C2×D8×C163 | C22 | semidirect |
| 64. C2×C163⋊C8 | D4 | semidirect |
| 86. M16×C163 | D4 | semidirect |
| 153. C163 | #3155 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D163 | semidirect |
| 177. C2×SD16 | C2×D163 | semidirect |
| 183. C2×D8 | C2×D163 | semidirect |
| 232. M16 | C22⋊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×#19104755 | 2 |
| C22×#14579684 | 2 |
| #23782232 | 2 |
| #23782229 | 2 |
| #23782053 | 2 |
| #23782051 | 2 |
| #23782046 | 2 |
| #23782040 | 2 |
| #23781623 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #3155 | 163 |