Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14579698 | C2 | semidirect |
| 2. C2×#19104756 | C2 | semidirect |
| 3. #23782178 | C2 | semidirect |
| 4. #23781824 | C2 | semidirect |
| 5. #23781820 | C2 | semidirect |
| 6. #23781811 | C2 | semidirect |
| 7. #23781806 | C2 | semidirect |
| 8. #23781799 | C2 | semidirect |
| 9. #23781658 | C2 | semidirect |
| 10. C22⋊C8×D163 | C2 | semidirect |
| 11. #450×C163 | C2 | semidirect |
| 12. C2×#14579700 | C22 | semidirect |
| 23. C2×#14579689 | C22 | semidirect |
| 24. C2×#14579688 | C22 | semidirect |
| 25. C2×#14579684 | C22 | semidirect |
| 26. C2×C8×D163 | C22 | semidirect |
| 28. #19104711 | C22 | semidirect |
| 29. #19104710 | C22 | semidirect |
| 34. #19104693 | C22 | semidirect |
| 35. #19104660 | C22 | semidirect |
| 36. #19104658 | C22 | semidirect |
| 37. #19104656 | C22 | semidirect |
| 39. (C2×D163)⋊C8 | C22 | semidirect |
| 41. C2×SD16×C163 | C22 | semidirect |
| 43. #102×C163 | C22 | semidirect |
| 52. #14579698 | D4 | semidirect |
| 147. C22×C163 | #135 | semidirect |
| 175. C163 | #3002 | semidirect |
| 182. #450 | D163 | semidirect |
| 202. C2×SD16 | C2×D163 | semidirect |
| 217. #102 | C2×D163 | semidirect |
| 333. C22 | #19104756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579698 | 2 |
| C2×#19104756 | 2 |
| #23782178 | 2 |
| #23781824 | 2 |
| #23781820 | 2 |
| #23781811 | 2 |
| #23781806 | 2 |
| #23781799 | 2 |
| #23781658 | 2 |
| C22⋊C8×D163 | 2 |
| #450×C163 | 2 |
| #3002 | 163 |