Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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. C2×#19104694 | C2 | semidirect |
| 3. #23781662 | C2 | direct (N × H) |
| 4. C2×#19104660 | C2 | semidirect |
| 5. C2×#19104657 | C2 | semidirect |
| 6. C23×C8×C163 | C2 | semidirect |
| 9. C2×#14579699 | C4 | semidirect |
| 16. #19104694 | C22 | semidirect |
| 20. #19104660 | C22 | semidirect |
| 21. #19104657 | C22 | semidirect |
| 25. C22×C8×C163 | C22 | semidirect |
| 29. #14579699 | C2×C4 | semidirect |
| 103. C2×C163 | #416 | semidirect |
| 107. C163 | C2×#416 | semidirect |
| 110. C23×C8 | D163 | semidirect |
| 126. C22×C8 | C2×D163 | semidirect |
| 212. C2 | #23781662 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579699 | 2 |
| C2×#19104694 | 2 |
| #23781662 | 2 |
| C2×#19104660 | 2 |
| C2×#19104657 | 2 |
| C23×C8×C163 | 2 |
| C2×#416 | 163 |