Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
388 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 77 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. C22⋊C8×D163 | C2 | semidirect |
| 3. #95×D163 | C2 | semidirect |
| 4. #23781400 | C2 | semidirect |
| 5. #23781399 | C2 | semidirect |
| 6. #23781398 | C2 | semidirect |
| 7. #327×C163 | C2 | semidirect |
| 9. C2×D4×D163 | C4 | semidirect |
| 13. #19104710 | C4 | semidirect |
| 17. #19104706 | C4 | semidirect |
| 18. C4⋊C4×D163 | C4 | semidirect |
| 20. C22⋊(C163⋊C8) | C22 | semidirect |
| 23. C163⋊#95 | C22 | semidirect |
| 25. C22⋊C8×C163 | C22 | semidirect |
| 26. #95×C163 | C22 | semidirect |
| 30. C2×D652 | C2×C4 | semidirect |
| 50. C4⋊Dic163 | C2×C4 | semidirect |
| 56. C2×D4×C163 | C2×C4 | semidirect |
| 60. C4⋊C4×C163 | C2×C4 | semidirect |
| 141. D163 | #327 | direct (N × H) |
| 142. C163 | C2×#327 | semidirect |
| 150. #327 | D163 | direct (N × H) |
| 166. C22⋊C8 | C2×D163 | semidirect |
| 169. #95 | C2×D163 | semidirect |
| 181. C2×D4 | C4×D163 | semidirect |
| 200. C4⋊C4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #121×D163 | 2 |
| C22⋊C8×D163 | 2 |
| #95×D163 | 2 |
| #23781400 | 2 |
| #23781399 | 2 |
| #23781398 | 2 |
| #327×C163 | 2 |
| C2×#327 | 163 |