Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
284 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 81 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. C2×C22⋊(C163⋊C8) | C2 | semidirect |
| 2. #23781528 | C2 | semidirect |
| 3. #23781402 | C2 | semidirect |
| 4. #23781399 | C2 | semidirect |
| 12. C2×#41×C163 | C4 | semidirect |
| 15. C22⋊Q8×C163 | C4 | semidirect |
| 17. #121×C163 | C4 | semidirect |
| 22. #117×C163 | C4 | semidirect |
| 111. C163 | #1516 | semidirect |
| 118. C2×#41 | Dic163 | semidirect |
| 122. C22⋊Q8 | Dic163 | semidirect |
| 124. #121 | Dic163 | semidirect |
| 129. #117 | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊(C163⋊C8) | 2 |
| #23781528 | 2 |
| #23781402 | 2 |
| #23781399 | 2 |
| #525×C163 | 2 |
| #1516 | 163 |