Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×Q16×D163 | C2 | semidirect |
| 3. C4⋊Q8×D163 | C2 | semidirect |
| 5. #23782060 | C2 | semidirect |
| 6. #23782059 | C2 | semidirect |
| 7. #23782058 | C2 | semidirect |
| 8. #23782057 | C2 | semidirect |
| 9. #23782056 | C2 | semidirect |
| 10. #97×D163 | C2 | semidirect |
| 11. #497×C163 | C2 | semidirect |
| 15. C2×Dic652 | C22 | semidirect |
| 16. C2×#14579689 | C22 | semidirect |
| 17. C2×#14579689 | C22 | semidirect |
| 24. #19104735 | C22 | semidirect |
| 26. #19104733 | C22 | semidirect |
| 34. #19104646 | C22 | semidirect |
| 35. #19104645 | C22 | semidirect |
| 36. C2×Q16×C163 | C22 | semidirect |
| 38. C4⋊Q8×C163 | C22 | semidirect |
| 40. #97×C163 | C22 | semidirect |
| 130. D163 | #497 | direct (N × H) |
| 131. C163 | C2×#497 | semidirect |
| 142. #497 | D163 | direct (N × H) |
| 151. C2×Q16 | C2×D163 | semidirect |
| 161. C4⋊Q8 | C2×D163 | semidirect |
| 172. #97 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D163 | 2 |
| C2×SD16×D163 | 2 |
| C4⋊Q8×D163 | 2 |
| #124×D163 | 2 |
| #23782060 | 2 |
| #23782059 | 2 |
| #23782058 | 2 |
| #23782057 | 2 |
| #23782056 | 2 |
| #97×D163 | 2 |
| #497×C163 | 2 |
| C2×#497 | 163 |