Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
924 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 2. C2×#19104697 | C2 | semidirect |
| 3. #23781566 | C2 | semidirect |
| 4. C42×Dic163 | C2 | semidirect |
| 5. #384×C163 | C2 | semidirect |
| 8. #19104732 | C4 | semidirect |
| 18. C2×D652 | C2×C4 | semidirect |
| 24. C4×Dic163 | D4 | semidirect |
| 28. C42×C163 | C2×C4 | semidirect |
| 49. C4×C163 | C4×D4 | semidirect |
| 51. Dic163 | #127 | semidirect |
| 56. C163 | C4×#127 | semidirect |
| 61. #384 | D163 | semidirect |
| 85. C42 | C4×D163 | semidirect |
| 108. C4 | #19104697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104732 | 2 |
| C2×#19104697 | 2 |
| #23781566 | 2 |
| C42×Dic163 | 2 |
| #384×C163 | 2 |
| C4×#127 | 163 |