Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
456 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 87 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. C22⋊C8×D163 | C2 | semidirect |
| 3. #23781389 | C2 | semidirect |
| 4. #23781388 | C2 | semidirect |
| 5. #323×C163 | C2 | semidirect |
| 15. C22⋊(C163⋊C8) | C22 | semidirect |
| 18. C22⋊C8×C163 | C22 | semidirect |
| 24. C23×D163 | C8 | semidirect |
| 62. C22×D163 | C2×C8 | semidirect |
| 77. C23×C163 | C2×C8 | semidirect |
| 121. D163 | #323 | direct (N × H) |
| 122. C163 | C2×#323 | semidirect |
| 128. #323 | D163 | direct (N × H) |
| 141. C22⋊C8 | C2×D163 | semidirect |
| 191. C23 | C8×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 |
| C22⋊C8×D163 | 2 |
| #23781389 | 2 |
| #23781388 | 2 |
| #323×C163 | 2 |
| C2×#323 | 163 |