Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
3464 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 429 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×C22⋊Dic163 | C2 | semidirect |
| 3. C22×(C2×D163)⋊C4 | C2 | semidirect |
| 4. #23781520 | C2 | direct (N × H) |
| 5. C22×C22⋊C4×C163 | C2 | semidirect |
| 9. C24×D163 | C4 | semidirect |
| 12. C23×Dic163 | C22 | semidirect |
| 14. C2×C22⋊Dic163 | C22 | semidirect |
| 16. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 18. C23×C4×C163 | C22 | semidirect |
| 20. C2×C22⋊C4×C163 | C22 | semidirect |
| 32. C23×D163 | C2×C4 | semidirect |
| 37. C22×Dic163 | C23 | semidirect |
| 48. C22×C4×C163 | C23 | semidirect |
| 62. C22×D163 | C22⋊C4 | semidirect |
| 72. C23×C163 | C22⋊C4 | semidirect |
| 90. C22×C163 | C2×C22⋊C4 | semidirect |
| 103. C2×D163 | C2×C22⋊C4 | semidirect |
| 107. C2×C163 | #379 | semidirect |
| 113. C163 | C2×#379 | semidirect |
| 118. C22×C22⋊C4 | D163 | semidirect |
| 128. C23×C4 | C2×D163 | semidirect |
| 134. C2×C22⋊C4 | C2×D163 | semidirect |
| 160. C22×C4 | C22×D163 | semidirect |
| 183. C23 | (C2×D163)⋊C4 | semidirect |
| 211. C22 | C2×(C2×D163)⋊C4 | semidirect |
| 222. C2 | #23781520 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D163 | 2 |
| C22×C22⋊Dic163 | 2 |
| C22×(C2×D163)⋊C4 | 2 |
| #23781520 | 2 |
| C22×C22⋊C4×C163 | 2 |
| C2×#379 | 163 |