Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23782142 | C2 | semidirect |
| 5. C2×#19104653 | C2 | semidirect |
| 6. #23781425 | C2 | semidirect |
| 7. #339×C163 | C2 | semidirect |
| 12. #19104723 | C4 | semidirect |
| 106. C163 | #1888 | semidirect |
| 114. #339 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104723 | 2 |
| #23782142 | 2 |
| #23781671 | 2 |
| #23781669 | 2 |
| C2×#19104653 | 2 |
| #23781425 | 2 |
| #339×C163 | 2 |
| #1888 | 163 |