Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782375 | C2 | semidirect |
| 3. #23782012 | C2 | semidirect |
| 4. #23781985 | C2 | semidirect |
| 5. #23781955 | C2 | semidirect |
| 6. #23781897 | C2 | semidirect |
| 7. #23781865 | C2 | semidirect |
| 8. #23781814 | C2 | semidirect |
| 9. C8×D652 | C2 | semidirect |
| 10. #102×D163 | C2 | semidirect |
| 11. C4×SD16×C163 | C2 | semidirect |
| 14. C2×#14579686 | C22 | semidirect |
| 15. C2×C8×D163 | C22 | semidirect |
| 16. #19104735 | C22 | semidirect |
| 20. #19104711 | C22 | semidirect |
| 26. C4⋊C4×D163 | C22 | semidirect |
| 27. #19104666 | C22 | semidirect |
| 28. C4⋊(C163⋊C8) | C22 | semidirect |
| 29. #19104657 | C22 | semidirect |
| 30. #19104657 | C22 | semidirect |
| 32. #19104655 | C22 | semidirect |
| 33. (C2×D163)⋊C8 | C22 | semidirect |
| 35. C4×Q8×C163 | C22 | semidirect |
| 37. #106×C163 | C22 | semidirect |
| 38. #103×C163 | C22 | semidirect |
| 40. C4×C8×C163 | C22 | semidirect |
| 88. D652 | SD16 | semidirect |
| 136. C163 | #3295 | semidirect |
| 146. C4×SD16 | D163 | semidirect |
| 162. C4×Q8 | C2×D163 | semidirect |
| 168. #106 | C2×D163 | semidirect |
| 170. #103 | C2×D163 | semidirect |
| 177. C4×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782375 | 2 |
| D4×D652 | 2 |
| #23782012 | 2 |
| #23781985 | 2 |
| #23781955 | 2 |
| #23781897 | 2 |
| #23781865 | 2 |
| #23781814 | 2 |
| C8×D652 | 2 |
| #102×D163 | 2 |
| C4×SD16×C163 | 2 |
| #3295 | 163 |