Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #23782034 | C2 | direct (N × H) |
| 54. C2×C163 | #491 | semidirect |
| 57. C163 | C2×#491 | semidirect |
| 112. C2 | #23782034 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104735 | 2 |
| C2×#19104727 | 2 |
| #23782034 | 2 |
| C2×#19104660 | 2 |
| C2×#97×C163 | 2 |
| C2×#491 | 163 |