Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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×#19104724 | C2 | semidirect |
| 3. C2×#19104711 | C2 | semidirect |
| 4. #23781582 | C2 | semidirect |
| 5. #23781572 | C2 | semidirect |
| 6. #23781567 | C2 | semidirect |
| 7. #23781536 | C2 | semidirect |
| 8. C4×(C2×D163)⋊C4 | C2 | semidirect |
| 9. C2×C4⋊Q8×C163 | C2 | semidirect |
| 106. C2×C4×C163 | #41 | semidirect |
| 136. C163 | #2432 | semidirect |
| 139. C2×C4⋊Q8 | D163 | semidirect |
| 243. C2×C4 | #14579700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579700 | 2 |
| C2×#19104724 | 2 |
| C2×#19104711 | 2 |
| #23781582 | 2 |
| #23781572 | 2 |
| #23781567 | 2 |
| #23781536 | 2 |
| C4×(C2×D163)⋊C4 | 2 |
| C2×C4⋊Q8×C163 | 2 |
| #2432 | 163 |