Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. C2×#19104667 | C2 | semidirect |
| 3. #23781433 | C2 | semidirect |
| 4. #23781430 | C2 | semidirect |
| 63. C163 | #2079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104667 | 2 |
| #23781666 | 2 |
| #23781433 | 2 |
| #23781430 | 2 |
| #408×C163 | 2 |
| #2079 | 163 |