Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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. #23782318 | C2 | semidirect |
| 2. D4×D652 | C2 | semidirect |
| 3. #23782013 | C2 | semidirect |
| 4. #23781980 | C2 | semidirect |
| 5. #23781902 | C2 | semidirect |
| 6. #23781861 | C2 | semidirect |
| 7. #23781800 | C2 | semidirect |
| 8. C4×#14579684 | C2 | semidirect |
| 9. #23781730 | C2 | semidirect |
| 10. #102×D163 | C2 | semidirect |
| 11. #474×C163 | C2 | semidirect |
| 15. C2×D1304 | C22 | semidirect |
| 17. C2×C8×D163 | C22 | semidirect |
| 22. #19104710 | C22 | semidirect |
| 26. C4×D652 | C22 | semidirect |
| 27. C4⋊C4×D163 | C22 | semidirect |
| 28. #19104668 | C22 | semidirect |
| 29. #19104657 | C22 | semidirect |
| 31. #19104655 | C22 | semidirect |
| 32. #19104655 | C22 | semidirect |
| 33. #19104655 | C22 | semidirect |
| 34. (C2×D163)⋊C8 | C22 | semidirect |
| 35. C4×C163⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C163 | C22 | semidirect |
| 38. #107×C163 | C22 | semidirect |
| 39. C4⋊C8×C163 | C22 | semidirect |
| 92. D652 | D8 | semidirect |
| 105. D4×C163 | #41 | semidirect |
| 142. C163 | #3294 | semidirect |
| 148. #474 | D163 | semidirect |
| 161. C4⋊Q8 | C2×D163 | semidirect |
| 174. #107 | C2×D163 | semidirect |
| 175. C4⋊C8 | C2×D163 | semidirect |
| 240. D4 | #14579700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782318 | 2 |
| D4×D652 | 2 |
| #23782013 | 2 |
| #23781980 | 2 |
| #23781902 | 2 |
| #23781861 | 2 |
| #23781800 | 2 |
| C4×#14579684 | 2 |
| #23781730 | 2 |
| #102×D163 | 2 |
| #474×C163 | 2 |
| #3294 | 163 |