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. #23781852 | C2 | semidirect |
| 3. #23781833 | C2 | semidirect |
| 4. #23781457 | C2 | semidirect |
| 5. #23781452 | C2 | semidirect |
| 6. #23781451 | C2 | semidirect |
| 7. B(4,𝔽2)×C163 | C2 | semidirect |
| 19. #19104652 | C22 | semidirect |
| 21. #19104650 | C22 | semidirect |
| 22. H(5,𝔽2)×C163 | C22 | semidirect |
| 26. #99×C163 | C22 | semidirect |
| 28. C23×D163 | D4 | semidirect |
| 30. C2×D652 | D4 | semidirect |
| 46. C22⋊Dic163 | D4 | semidirect |
| 50. C4×Dic163 | D4 | semidirect |
| 51. C24×C163 | D4 | semidirect |
| 63. C22⋊C4×C163 | D4 | semidirect |
| 143. C163 | #2196 | semidirect |
| 147. B(4,𝔽2) | D163 | semidirect |
| 152. H(5,𝔽2) | C2×D163 | semidirect |
| 170. #99 | C2×D163 | semidirect |
| 173. C24 | C22⋊D163 | semidirect |
| 206. C22⋊C4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782297 | 2 |
| #23781852 | 2 |
| #23781833 | 2 |
| #23781457 | 2 |
| #23781452 | 2 |
| #23781451 | 2 |
| B(4,𝔽2)×C163 | 2 |
| #2196 | 163 |