Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
354 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 41 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. #23782297 | C2 | semidirect |
| 2. #23781853 | C2 | semidirect |
| 3. #23781851 | C2 | semidirect |
| 4. #23781835 | C2 | semidirect |
| 5. #23781457 | C2 | semidirect |
| 6. #23781453 | C2 | semidirect |
| 7. AΣL(1,𝔽16)×C163 | C2 | semidirect |
| 8. #19104780 | C22 | semidirect |
| 21. #19104650 | C22 | semidirect |
| 25. #100×C163 | C22 | semidirect |
| 26. #99×C163 | C22 | semidirect |
| 28. C23×D163 | D4 | semidirect |
| 33. C2×D652 | D4 | semidirect |
| 52. C22⋊Dic163 | D4 | semidirect |
| 56. C4×Dic163 | D4 | semidirect |
| 57. C24×C163 | D4 | semidirect |
| 63. C22⋊C4×C163 | D4 | semidirect |
| 143. C163 | #2196 | semidirect |
| 151. AΣL(1,𝔽16) | D163 | semidirect |
| 166. #100 | C2×D163 | semidirect |
| 170. #99 | C2×D163 | semidirect |
| 173. C24 | D652 | semidirect |
| 206. C22⋊C4 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782297 | 2 |
| #23781853 | 2 |
| #23781851 | 2 |
| #23781835 | 2 |
| #23781457 | 2 |
| #23781453 | 2 |
| AΣL(1,𝔽16)×C163 | 2 |
| #2196 | 163 |