Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×#14579699 | C2 | semidirect |
| 2. C2×#19104763 | C2 | semidirect |
| 3. C2×#19104709 | C2 | semidirect |
| 4. #23781812 | C2 | semidirect |
| 5. #23781806 | C2 | semidirect |
| 6. #23781801 | C2 | semidirect |
| 7. #23781667 | C2 | semidirect |
| 8. #407×C163 | C2 | semidirect |
| 13. C2×#14579699 | C22 | semidirect |
| 14. C22×Dic326 | C22 | semidirect |
| 15. C22×D652 | C22 | semidirect |
| 16. C22×D652 | C22 | semidirect |
| 21. C2×#14579688 | C22 | semidirect |
| 22. C2×D1304 | C22 | semidirect |
| 26. #19104709 | C22 | semidirect |
| 27. C2×C4⋊Dic163 | C22 | semidirect |
| 29. #19104660 | C22 | semidirect |
| 30. #19104657 | C22 | semidirect |
| 32. C2×M16×C163 | C22 | semidirect |
| 33. C22⋊C8×C163 | C22 | semidirect |
| 34. C22⋊C8×C163 | C22 | semidirect |
| 42. #14579699 | D4 | semidirect |
| 89. Dic326 | C2×D4 | semidirect |
| 94. D652 | C2×D4 | semidirect |
| 131. C22×C163 | AGL(1,ℤ/8) | semidirect |
| 155. C163 | #3006 | semidirect |
| 164. #407 | D163 | semidirect |
| 180. C2×M16 | C2×D163 | semidirect |
| 189. C22⋊C8 | C2×D163 | semidirect |
| 190. C22⋊C8 | C2×D163 | semidirect |
| 295. C22 | #19104763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579699 | 2 |
| C2×#19104763 | 2 |
| C2×#19104709 | 2 |
| #23781812 | 2 |
| #23781806 | 2 |
| #23781801 | 2 |
| #23781667 | 2 |
| #407×C163 | 2 |
| #3006 | 163 |