Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782009 | C2 | semidirect |
| 4. #23782008 | C2 | semidirect |
| 5. #23782002 | C2 | semidirect |
| 6. #23781997 | C2 | semidirect |
| 7. #23781701 | C2 | semidirect |
| 8. #23781675 | C2 | semidirect |
| 9. C2×#19104658 | C2 | semidirect |
| 11. #428×C163 | C2 | semidirect |
| 126. C163 | #3097 | semidirect |
| 134. #428 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782241 | 2 |
| #23782146 | 2 |
| #23782009 | 2 |
| #23782008 | 2 |
| #23782002 | 2 |
| #23781997 | 2 |
| #23781701 | 2 |
| #23781675 | 2 |
| C2×#19104658 | 2 |
| #23781633 | 2 |
| #428×C163 | 2 |
| #3097 | 163 |