Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 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. C22×#14579700 | C2 | semidirect |
| 2. C2×#19104760 | C2 | semidirect |
| 3. #23782172 | C2 | semidirect |
| 4. #23781826 | C2 | semidirect |
| 5. #23781809 | C2 | semidirect |
| 6. #23781674 | C2 | semidirect |
| 7. #23781671 | C2 | semidirect |
| 8. #23781628 | C2 | semidirect |
| 9. C2×#137×C163 | C2 | semidirect |
| 19. C2×#14579686 | C22 | semidirect |
| 20. C2×#14579684 | C22 | semidirect |
| 23. #19104711 | C22 | semidirect |
| 24. #19104706 | C22 | semidirect |
| 28. #19104659 | C22 | semidirect |
| 29. #19104657 | C22 | semidirect |
| 30. (C2×D163)⋊C8 | C22 | semidirect |
| 34. C2×Q16×C163 | C22 | semidirect |
| 35. C2×SD16×C163 | C22 | semidirect |
| 46. C2×D652 | D4 | semidirect |
| 70. C2×Q8×C163 | D4 | semidirect |
| 145. C163 | #3005 | semidirect |
| 148. C2×#137 | D163 | semidirect |
| 168. C2×Q16 | C2×D163 | semidirect |
| 170. C2×SD16 | C2×D163 | semidirect |
| 192. C2×Q8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579700 | 2 |
| C2×#19104760 | 2 |
| #23782172 | 2 |
| #23781826 | 2 |
| #23781809 | 2 |
| #23781674 | 2 |
| #23781671 | 2 |
| #23781628 | 2 |
| C2×#137×C163 | 2 |
| #3005 | 163 |