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. C23×C163⋊C8 | C2 | semidirect |
| 3. #23781659 | C2 | direct (N × H) |
| 4. C2×#19104658 | C2 | semidirect |
| 5. C2×#19104655 | C2 | semidirect |
| 6. C2×#117×C163 | C2 | semidirect |
| 9. C2×#14579699 | C4 | semidirect |
| 17. C22×C163⋊C8 | C22 | semidirect |
| 18. #19104658 | C22 | semidirect |
| 19. #19104655 | C22 | semidirect |
| 22. #117×C163 | C22 | semidirect |
| 29. #14579699 | C2×C4 | semidirect |
| 103. C2×C163 | #416 | semidirect |
| 107. C163 | C2×#416 | semidirect |
| 111. C2×#117 | D163 | semidirect |
| 128. #117 | C2×D163 | semidirect |
| 212. C2 | #23781659 | 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 |
| C23×C163⋊C8 | 2 |
| #23781659 | 2 |
| C2×#19104658 | 2 |
| C2×#19104655 | 2 |
| C2×#117×C163 | 2 |
| C2×#416 | 163 |