Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 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. #23782148 | C2 | semidirect |
| 3. #23781675 | C2 | semidirect |
| 4. #23781667 | C2 | semidirect |
| 5. #23781662 | C2 | semidirect |
| 6. C2×#19104660 | C2 | semidirect |
| 7. C2×#131×C163 | C2 | semidirect |
| 9. #19104782 | C4 | semidirect |
| 28. #14579699 | C2×C4 | semidirect |
| 32. C2×Dic326 | C2×C4 | semidirect |
| 94. C163 | #2898 | semidirect |
| 97. C2×#131 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104782 | 2 |
| #23782148 | 2 |
| #23781675 | 2 |
| #23781667 | 2 |
| #23781662 | 2 |
| C2×#19104660 | 2 |
| C2×#131×C163 | 2 |
| #2898 | 163 |