Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 229 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×C22⋊C4×D163 | C2 | semidirect |
| 3. #23781543 | C2 | semidirect |
| 4. #23781528 | C2 | semidirect |
| 5. #23781520 | C2 | semidirect |
| 6. #381×C163 | C2 | semidirect |
| 10. C22×D652 | C4 | semidirect |
| 12. C22×C4×D163 | C22 | semidirect |
| 14. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 15. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 17. C163⋊#95 | C22 | semidirect |
| 20. #95×C163 | C22 | semidirect |
| 25. C23×D163 | C2×C4 | semidirect |
| 32. C2×D652 | C2×C4 | semidirect |
| 41. C22×C4×C163 | C2×C4 | semidirect |
| 53. C22×D163 | C22⋊C4 | semidirect |
| 95. C163 | #2308 | semidirect |
| 101. #381 | D163 | semidirect |
| 116. #95 | C2×D163 | semidirect |
| 134. C22×C4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D652 | 2 |
| C2×C22⋊C4×D163 | 2 |
| #23781543 | 2 |
| #23781528 | 2 |
| #23781520 | 2 |
| #381×C163 | 2 |
| #2308 | 163 |