Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23781990 | C2 | semidirect |
| 5. #23781707 | C2 | semidirect |
| 6. #23781667 | C2 | semidirect |
| 7. #407×C163 | C2 | semidirect |
| 20. #19104669 | C22 | semidirect |
| 21. #19104667 | C22 | semidirect |
| 22. #19104660 | C22 | semidirect |
| 23. #19104657 | C22 | semidirect |
| 94. C163 | #3093 | semidirect |
| 102. #407 | 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 |
| #23781990 | 2 |
| #23781707 | 2 |
| #23781667 | 2 |
| #407×C163 | 2 |
| #3093 | 163 |