Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23782032 | C2 | semidirect |
| 4. #23782014 | C2 | semidirect |
| 100. C163 | #3139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782218 | 2 |
| C2×#19104733 | 2 |
| #23782032 | 2 |
| #23782014 | 2 |
| #23781675 | 2 |
| #23781674 | 2 |
| #23781673 | 2 |
| M16×Dic163 | 2 |
| #419×C163 | 2 |
| #3139 | 163 |