Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 762 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×#19104780 | C2 | semidirect |
| 2. #23782465 | C2 | semidirect |
| 3. #23782232 | C2 | semidirect |
| 4. #23781845 | C2 | semidirect |
| 5. #23781835 | C2 | semidirect |
| 6. #23781681 | C2 | semidirect |
| 7. C2×#100×C163 | C2 | semidirect |
| 12. C2×#14579699 | C22 | semidirect |
| 17. #19104768 | C22 | semidirect |
| 19. #19104763 | C22 | semidirect |
| 21. #19104731 | C22 | semidirect |
| 22. #19104722 | C22 | semidirect |
| 25. #19104694 | C22 | semidirect |
| 26. #19104661 | C22 | semidirect |
| 28. C2×M16×C163 | C22 | semidirect |
| 29. #100×C163 | C22 | semidirect |
| 35. #14579699 | D4 | semidirect |
| 39. C2×Dic326 | D4 | semidirect |
| 40. C2×Dic326 | C23 | semidirect |
| 41. C2×D652 | D4 | semidirect |
| 42. C2×D652 | C23 | semidirect |
| 61. C4×Dic163 | C23 | semidirect |
| 69. M16×C163 | C23 | semidirect |
| 131. C163 | #3019 | semidirect |
| 139. C2×#100 | D163 | semidirect |
| 154. C2×M16 | C2×D163 | semidirect |
| 161. #100 | C2×D163 | semidirect |
| 197. M16 | C22×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104780 | 2 |
| #23782465 | 2 |
| #23782232 | 2 |
| #23781845 | 2 |
| #23781835 | 2 |
| #23781681 | 2 |
| C2×#100×C163 | 2 |
| #3019 | 163 |