Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
246 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 51 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. #23781984 | C2 | semidirect |
| 3. #23781981 | C2 | semidirect |
| 4. #23781605 | C2 | semidirect |
| 5. #23781398 | C2 | semidirect |
| 6. #23781390 | C2 | semidirect |
| 7. #327×C163 | C2 | semidirect |
| 113. C163 | #1616 | semidirect |
| 120. #327 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782242 | 2 |
| #23781984 | 2 |
| #23781981 | 2 |
| #23781605 | 2 |
| #23781398 | 2 |
| #23781390 | 2 |
| #327×C163 | 2 |
| #1616 | 163 |