Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
480 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 205 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. #23781770 | C2 | direct (N × H) |
| 10. C2×#14579689 | C4 | semidirect |
| 36. #14579689 | C2×C4 | semidirect |
| 98. C2×C163 | #441 | semidirect |
| 102. C163 | C2×#441 | semidirect |
| 201. C2 | #23781770 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579689 | 2 |
| C2×C4×Dic326 | 2 |
| #23781770 | 2 |
| C2×#19104666 | 2 |
| C2×#19104659 | 2 |
| C2×#19104658 | 2 |
| C2×#19104646 | 2 |
| C2×C4×Q8×C163 | 2 |
| C2×#441 | 163 |