Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 448 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. #23782217 | C2 | semidirect |
| 3. #23781995 | C2 | semidirect |
| 4. #23781954 | C2 | semidirect |
| 5. #23781869 | C2 | semidirect |
| 8. #23781752 | C2 | semidirect |
| 9. #23781750 | C2 | semidirect |
| 10. #23781715 | C2 | semidirect |
| 11. #483×C163 | C2 | semidirect |
| 16. #19104734 | C22 | semidirect |
| 17. #19104733 | C22 | semidirect |
| 21. Q8×Dic163 | C22 | semidirect |
| 23. #19104700 | C22 | semidirect |
| 31. #19104666 | C22 | semidirect |
| 32. Dic163⋊C8 | C22 | semidirect |
| 33. #19104658 | C22 | semidirect |
| 37. C8×Dic163 | C22 | semidirect |
| 40. #106×C163 | C22 | semidirect |
| 41. #103×C163 | C22 | semidirect |
| 94. C2×Dic163 | SD16 | semidirect |
| 136. C163 | #3101 | semidirect |
| 141. #483 | D163 | semidirect |
| 171. #106 | C2×D163 | semidirect |
| 174. #103 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782217 | 2 |
| C2×#19104697 | 2 |
| #23781995 | 2 |
| #23781954 | 2 |
| #23781869 | 2 |
| #23781818 | 2 |
| #23781815 | 2 |
| #23781752 | 2 |
| #23781750 | 2 |
| #23781715 | 2 |
| #483×C163 | 2 |
| #3101 | 163 |