Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23782065 | C2 | semidirect |
| 3. #23782043 | C2 | semidirect |
| 4. #23782032 | C2 | semidirect |
| 8. #23781773 | C2 | semidirect |
| 9. C4×#14579689 | C2 | semidirect |
| 11. #441×C163 | C2 | semidirect |
| 103. C163 | #3177 | semidirect |
| 113. #441 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782273 | 2 |
| #23782065 | 2 |
| #23782043 | 2 |
| #23782032 | 2 |
| #23781924 | 2 |
| #23781920 | 2 |
| #23781905 | 2 |
| #23781773 | 2 |
| C4×#14579689 | 2 |
| #23781622 | 2 |
| #441×C163 | 2 |
| #3177 | 163 |