Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1088 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 285 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×#19104694 | C2 | semidirect |
| 3. #23781526 | C2 | semidirect |
| 4. #23781522 | C2 | semidirect |
| 6. C4×(C2×D163)⋊C4 | C2 | semidirect |
| 7. C2×#117×C163 | C2 | semidirect |
| 12. C22×C4×D163 | C4 | semidirect |
| 16. C2×C4⋊Dic163 | C22 | semidirect |
| 19. C2×C4×Dic163 | C22 | semidirect |
| 20. C163⋊#95 | C22 | semidirect |
| 23. C2×C4⋊C4×C163 | C22 | semidirect |
| 25. C2×C42×C163 | C22 | semidirect |
| 81. C2×C4×C163 | C22⋊C4 | semidirect |
| 101. C2×D163 | #117 | semidirect |
| 113. C163 | #2280 | semidirect |
| 117. C2×#117 | D163 | semidirect |
| 133. C2×C4⋊C4 | C2×D163 | semidirect |
| 138. C2×C42 | C2×D163 | semidirect |
| 195. C2×C4 | (C2×D163)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D163 | 2 |
| C2×#19104694 | 2 |
| #23781526 | 2 |
| #23781522 | 2 |
| #23781520 | 2 |
| C4×(C2×D163)⋊C4 | 2 |
| C2×#117×C163 | 2 |
| #2280 | 163 |