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×#14579700 | C2 | semidirect |
| 2. C2×#19104758 | C2 | semidirect |
| 3. #23782178 | C2 | semidirect |
| 4. #23781826 | C2 | semidirect |
| 5. #23781815 | C2 | semidirect |
| 6. #23781813 | C2 | semidirect |
| 7. #23781804 | C2 | semidirect |
| 8. #23781801 | C2 | semidirect |
| 9. #23781660 | C2 | semidirect |
| 10. C22⋊C8×D163 | C2 | semidirect |
| 11. #451×C163 | C2 | semidirect |
| 17. C2×#14579700 | C22 | semidirect |
| 23. C2×#14579686 | C22 | semidirect |
| 24. C2×#14579686 | C22 | semidirect |
| 25. C2×D1304 | C22 | semidirect |
| 26. C2×C8×D163 | C22 | semidirect |
| 28. #19104711 | C22 | semidirect |
| 29. #19104710 | C22 | semidirect |
| 34. #19104693 | C22 | semidirect |
| 35. #19104659 | C22 | semidirect |
| 36. #19104657 | C22 | semidirect |
| 37. #19104655 | C22 | semidirect |
| 39. (C2×D163)⋊C8 | C22 | semidirect |
| 41. C2×Q16×C163 | C22 | semidirect |
| 43. #103×C163 | C22 | semidirect |
| 53. #14579700 | D4 | semidirect |
| 143. C22×C163 | #135 | semidirect |
| 175. C163 | #3002 | semidirect |
| 181. #451 | D163 | semidirect |
| 200. C2×Q16 | C2×D163 | semidirect |
| 215. #103 | C2×D163 | semidirect |
| 333. C22 | #19104758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579700 | 2 |
| C2×#19104758 | 2 |
| #23782178 | 2 |
| #23781826 | 2 |
| #23781815 | 2 |
| #23781813 | 2 |
| #23781804 | 2 |
| #23781801 | 2 |
| #23781660 | 2 |
| C22⋊C8×D163 | 2 |
| #451×C163 | 2 |
| #3002 | 163 |