Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19104764 | C2 | semidirect |
| 2. C2×#19104759 | C2 | semidirect |
| 3. #23782213 | C2 | semidirect |
| 4. #124×D163 | C2 | semidirect |
| 5. #23782060 | C2 | semidirect |
| 6. #23782059 | C2 | semidirect |
| 7. #23782052 | C2 | semidirect |
| 8. #23782048 | C2 | semidirect |
| 9. #23782046 | C2 | semidirect |
| 10. #23781617 | C2 | semidirect |
| 11. #496×C163 | C2 | semidirect |
| 17. C2×Dic652 | C22 | semidirect |
| 18. C2×#14579689 | C22 | semidirect |
| 21. C2×#14579687 | C22 | semidirect |
| 24. #19104735 | C22 | semidirect |
| 28. #19104722 | C22 | semidirect |
| 34. #19104646 | C22 | semidirect |
| 35. C8×Dic163 | C22 | semidirect |
| 36. C2×SD16×C163 | C22 | semidirect |
| 38. #127×C163 | C22 | semidirect |
| 40. #97×C163 | C22 | semidirect |
| 62. #14579682 | D4 | semidirect |
| 134. C163 | #3153 | semidirect |
| 143. #496 | D163 | semidirect |
| 157. C2×SD16 | C2×D163 | semidirect |
| 162. #127 | C2×D163 | semidirect |
| 174. #97 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104764 | 2 |
| C2×#19104759 | 2 |
| #23782213 | 2 |
| #124×D163 | 2 |
| #23782060 | 2 |
| #23782059 | 2 |
| #23782052 | 2 |
| #23782048 | 2 |
| #23782046 | 2 |
| #23781617 | 2 |
| #496×C163 | 2 |
| #3153 | 163 |