Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
680 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23781432 | C2 | semidirect |
| 4. #23781431 | C2 | semidirect |
| 5. #342×C163 | C2 | semidirect |
| 8. C22×C4×D163 | C4 | semidirect |
| 12. C2×(C2×D163)⋊C4 | C4 | semidirect |
| 16. C22⋊C4×D163 | C4 | semidirect |
| 28. C22×Dic163 | C2×C4 | semidirect |
| 36. C22⋊Dic163 | C2×C4 | semidirect |
| 41. C22×C4×C163 | C2×C4 | semidirect |
| 44. C22⋊C4×C163 | C2×C4 | semidirect |
| 116. D163 | #342 | direct (N × H) |
| 117. C163 | C2×#342 | semidirect |
| 123. #342 | D163 | direct (N × H) |
| 154. C22×C4 | C4×D163 | semidirect |
| 162. C22⋊C4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊C4×D163 | 2 |
| #23781432 | 2 |
| #23781431 | 2 |
| #342×C163 | 2 |
| C2×#342 | 163 |