Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
814 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 165 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×(C2×D163)⋊C4 | C2 | semidirect |
| 3. C2×C22⋊C4×D163 | C2 | semidirect |
| 4. #23781591 | C2 | semidirect |
| 5. #23781581 | C2 | semidirect |
| 6. #23781545 | C2 | semidirect |
| 7. #23781541 | C2 | semidirect |
| 8. #23781540 | C2 | semidirect |
| 9. #23781528 | C2 | semidirect |
| 10. #23781522 | C2 | semidirect |
| 11. C2×#123×C163 | C2 | semidirect |
| 18. C2×C4⋊Dic163 | C22 | semidirect |
| 21. C2×C22⋊Dic163 | C22 | semidirect |
| 29. C163⋊#95 | C22 | semidirect |
| 30. C163⋊#95 | C22 | semidirect |
| 31. C163⋊#95 | C22 | semidirect |
| 32. C163⋊#95 | C22 | semidirect |
| 36. C2×C4⋊C4×C163 | C22 | semidirect |
| 38. C2×C22⋊C4×C163 | C22 | semidirect |
| 81. C22⋊C4×C163 | D4 | semidirect |
| 158. C2×D163 | #123 | semidirect |
| 175. C163 | #2412 | semidirect |
| 177. C2×#123 | D163 | semidirect |
| 198. C2×C4⋊C4 | C2×D163 | semidirect |
| 210. C2×C22⋊C4 | C2×D163 | semidirect |
| 257. C22⋊C4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104703 | 2 |
| C22×(C2×D163)⋊C4 | 2 |
| C2×C22⋊C4×D163 | 2 |
| #23781591 | 2 |
| #23781581 | 2 |
| #23781545 | 2 |
| #23781541 | 2 |
| #23781540 | 2 |
| #23781528 | 2 |
| #23781522 | 2 |
| C2×#123×C163 | 2 |
| #2412 | 163 |