Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19104694 | C2 | semidirect |
| 3. #23782007 | C2 | semidirect |
| 4. #23782001 | C2 | semidirect |
| 5. #23781996 | C2 | semidirect |
| 6. #23781990 | C2 | semidirect |
| 7. #23781984 | C2 | semidirect |
| 8. #23781979 | C2 | semidirect |
| 9. #23781703 | C2 | semidirect |
| 10. #23781662 | C2 | semidirect |
| 11. C2×C22⋊C8×C163 | C2 | semidirect |
| 30. #19104669 | C22 | semidirect |
| 31. #19104669 | C22 | semidirect |
| 32. #19104667 | C22 | semidirect |
| 33. #19104667 | C22 | semidirect |
| 34. #19104660 | C22 | semidirect |
| 35. #19104660 | C22 | semidirect |
| 36. #19104657 | C22 | semidirect |
| 37. #19104657 | C22 | semidirect |
| 143. C163 | #3091 | semidirect |
| 155. C2×C22⋊C8 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782176 | 2 |
| C2×#19104694 | 2 |
| #23782007 | 2 |
| #23782001 | 2 |
| #23781996 | 2 |
| #23781990 | 2 |
| #23781984 | 2 |
| #23781979 | 2 |
| #23781703 | 2 |
| #23781662 | 2 |
| C2×C22⋊C8×C163 | 2 |
| #3091 | 163 |