Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23781627 | C2 | semidirect |
| 3. #95×D163 | C2 | semidirect |
| 4. #23781403 | C2 | semidirect |
| 5. #23781401 | C2 | semidirect |
| 6. #23781399 | C2 | semidirect |
| 7. #327×C163 | C2 | semidirect |
| 8. C2×#14579698 | C4 | semidirect |
| 13. #19104715 | C4 | semidirect |
| 15. #19104706 | C4 | semidirect |
| 19. #19104693 | C4 | semidirect |
| 29. C2×Dic326 | C2×C4 | semidirect |
| 46. C4⋊Dic163 | C2×C4 | semidirect |
| 54. C2×D4×C163 | C2×C4 | semidirect |
| 58. C4⋊C4×C163 | C2×C4 | semidirect |
| 130. C163 | #1504 | semidirect |
| 138. #327 | D163 | semidirect |
| 164. C2×D4 | C4×D163 | semidirect |
| 184. C4⋊C4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782175 | 2 |
| #23781627 | 2 |
| #95×D163 | 2 |
| #23781403 | 2 |
| #23781401 | 2 |
| #23781399 | 2 |
| #327×C163 | 2 |
| #1504 | 163 |