Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×#19104659 | C2 | semidirect |
| 5. C2×#19104645 | C2 | semidirect |
| 6. #23781534 | C2 | semidirect |
| 7. C2×#103×C163 | C2 | semidirect |
| 11. #19104724 | C4 | semidirect |
| 112. C163 | #1959 | semidirect |
| 116. C2×#103 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104724 | 2 |
| C2×#19104659 | 2 |
| C2×#19104657 | 2 |
| C2×#19104655 | 2 |
| C2×#19104645 | 2 |
| #23781534 | 2 |
| C2×#103×C163 | 2 |
| #1959 | 163 |