Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
310 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 310 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 |
|---|---|---|
| 1. #23782242 | C2 | semidirect |
| 2. #23781801 | C2 | semidirect |
| 3. #23781798 | C2 | semidirect |
| 4. #23781583 | C2 | semidirect |
| 5. #23781398 | C2 | semidirect |
| 6. #23781390 | C2 | semidirect |
| 7. #327×C163 | C2 | semidirect |
| 85. C2×Dic163 | D8 | semidirect |
| 134. C163 | #1598 | semidirect |
| 141. #327 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782242 | 2 |
| #23781801 | 2 |
| #23781798 | 2 |
| #23781583 | 2 |
| #23781398 | 2 |
| #23781390 | 2 |
| #327×C163 | 2 |
| #1598 | 163 |