Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
800 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 800 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×#19104780 | C2 | semidirect |
| 2. #23782227 | C2 | semidirect |
| 3. #23782224 | C2 | semidirect |
| 4. #23781856 | C2 | semidirect |
| 5. #23781853 | C2 | semidirect |
| 6. C2×#19104649 | C2 | semidirect |
| 7. C2×#99×C163 | C2 | semidirect |
| 15. C22×C22⋊D163 | C22 | semidirect |
| 18. #19104719 | C22 | semidirect |
| 20. #19104716 | C22 | semidirect |
| 24. #19104705 | C22 | semidirect |
| 26. #19104703 | C22 | semidirect |
| 27. C2×C22⋊Dic163 | C22 | semidirect |
| 28. #19104649 | C22 | semidirect |
| 30. C2×C22⋊C4×C163 | C22 | semidirect |
| 31. #99×C163 | C22 | semidirect |
| 33. C23×D163 | D4 | semidirect |
| 34. C23×D163 | C23 | semidirect |
| 54. C2×C22⋊D163 | D4 | semidirect |
| 60. C22×Dic163 | D4 | semidirect |
| 61. C22×Dic163 | C23 | semidirect |
| 67. C22⋊Dic163 | C23 | semidirect |
| 71. C24×C163 | D4 | semidirect |
| 75. C2×D4×C163 | D4 | semidirect |
| 78. C22×C4×C163 | D4 | semidirect |
| 80. C22⋊C4×C163 | C23 | semidirect |
| 164. C163 | #3026 | semidirect |
| 172. C2×#99 | D163 | semidirect |
| 194. C2×C22⋊C4 | C2×D163 | semidirect |
| 196. #99 | C2×D163 | semidirect |
| 200. C24 | D652 | semidirect |
| 227. C2×D4 | D652 | semidirect |
| 235. C22×C4 | D652 | semidirect |
| 245. C22⋊C4 | C22×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104780 | 2 |
| #23782227 | 2 |
| #23782224 | 2 |
| #23781856 | 2 |
| #23781853 | 2 |
| C2×#19104649 | 2 |
| C2×#99×C163 | 2 |
| #3026 | 163 |