Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
432 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. C22×C8×D163 | C2 | semidirect |
| 3. C2×(C2×D163)⋊C8 | C2 | semidirect |
| 4. C2×(C2×D163)⋊C8 | C2 | semidirect |
| 5. C2×(C2×D163)⋊C8 | C2 | semidirect |
| 6. #23781420 | C2 | semidirect |
| 7. #336×C163 | C2 | semidirect |
| 31. C2×D652 | C8 | semidirect |
| 51. C2×C163⋊C8 | D4 | semidirect |
| 64. C2×C8×C163 | D4 | semidirect |
| 79. C22×D163 | C2×C8 | semidirect |
| 104. C2×C4×C163 | C2×C8 | semidirect |
| 133. C2×D163 | C22⋊C8 | semidirect |
| 151. C163 | #1869 | semidirect |
| 159. #336 | D163 | semidirect |
| 213. C2×C8 | D652 | semidirect |
| 254. C2×C4 | C8×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D163 | 2 |
| C2×C4×D652 | 2 |
| C2×(C2×D163)⋊C8 | 2 |
| #23781420 | 2 |
| #336×C163 | 2 |
| #1869 | 163 |