Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23781719 | C2 | semidirect |
| 3. #23781715 | C2 | semidirect |
| 4. #23781390 | C2 | semidirect |
| 5. #23781390 | C2 | semidirect |
| 106. C163 | #1473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104728 | 2 |
| #23781719 | 2 |
| #23781715 | 2 |
| #23781390 | 2 |
| #23781389 | 2 |
| #323×C163 | 2 |
| #1473 | 163 |