Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782210 | C2 | semidirect |
| 2. C2×#19104697 | C2 | semidirect |
| 3. #23781978 | C2 | semidirect |
| 4. #23781944 | C2 | semidirect |
| 5. #23781859 | C2 | semidirect |
| 6. #23781801 | C2 | semidirect |
| 7. #23781798 | C2 | semidirect |
| 8. #23781747 | C2 | semidirect |
| 9. #23781745 | C2 | semidirect |
| 10. #23781715 | C2 | semidirect |
| 11. #480×C163 | C2 | semidirect |
| 17. #19104734 | C22 | semidirect |
| 18. #19104731 | C22 | semidirect |
| 22. D4×Dic163 | C22 | semidirect |
| 27. #19104697 | C22 | semidirect |
| 31. #19104668 | C22 | semidirect |
| 32. Dic163⋊C8 | C22 | semidirect |
| 35. #19104655 | C22 | semidirect |
| 37. C8×Dic163 | C22 | semidirect |
| 40. #107×C163 | C22 | semidirect |
| 41. #102×C163 | C22 | semidirect |
| 92. D652 | #41 | semidirect |
| 99. C2×Dic163 | D8 | semidirect |
| 149. C163 | #3100 | semidirect |
| 154. #480 | D163 | semidirect |
| 184. #107 | C2×D163 | semidirect |
| 189. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782210 | 2 |
| C2×#19104697 | 2 |
| #23781978 | 2 |
| #23781944 | 2 |
| #23781859 | 2 |
| #23781801 | 2 |
| #23781798 | 2 |
| #23781747 | 2 |
| #23781745 | 2 |
| #23781715 | 2 |
| #480×C163 | 2 |
| #3100 | 163 |