Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 1. D4×D652 | C2 | semidirect |
| 2. #23782013 | C2 | semidirect |
| 3. #23781978 | C2 | semidirect |
| 4. #23781942 | C2 | semidirect |
| 5. #23781899 | C2 | semidirect |
| 6. #23781860 | C2 | semidirect |
| 7. #23781798 | C2 | semidirect |
| 8. C4×#14579684 | C2 | semidirect |
| 9. D4×C163⋊C8 | C2 | semidirect |
| 10. C2×#19104655 | C2 | semidirect |
| 11. #547×C163 | C2 | semidirect |
| 15. C2×#14579684 | C22 | semidirect |
| 16. C22×C163⋊C8 | C22 | semidirect |
| 22. #19104668 | C22 | semidirect |
| 23. #19104668 | C22 | semidirect |
| 24. C4⋊(C163⋊C8) | C22 | semidirect |
| 25. #19104656 | C22 | semidirect |
| 28. #19104655 | C22 | semidirect |
| 29. #19104655 | C22 | semidirect |
| 30. #19104655 | C22 | semidirect |
| 31. C22⋊(C163⋊C8) | C22 | semidirect |
| 32. C4×C163⋊C8 | C22 | semidirect |
| 34. C4⋊Q8×C163 | C22 | semidirect |
| 37. #121×C163 | C22 | semidirect |
| 39. C4×D4×C163 | C22 | semidirect |
| 40. C2×C4⋊C4×C163 | C22 | semidirect |
| 89. D652 | #41 | semidirect |
| 102. D4×C163 | D8 | semidirect |
| 142. C163 | #3294 | semidirect |
| 144. #547 | D163 | semidirect |
| 161. C4⋊Q8 | C2×D163 | semidirect |
| 167. #121 | C2×D163 | semidirect |
| 171. C4×D4 | C2×D163 | semidirect |
| 172. C2×C4⋊C4 | C2×D163 | semidirect |
| 240. D4 | #14579684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D652 | 2 |
| #23782013 | 2 |
| #23781978 | 2 |
| #23781942 | 2 |
| #23781899 | 2 |
| #23781860 | 2 |
| #23781798 | 2 |
| C4×#14579684 | 2 |
| D4×C163⋊C8 | 2 |
| C2×#19104655 | 2 |
| #547×C163 | 2 |
| #3294 | 163 |