Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
480 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 181 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×#19104735 | C2 | semidirect |
| 2. #23781945 | C2 | direct (N × H) |
| 3. C2×#19104668 | C2 | semidirect |
| 4. C2×C4⋊(C163⋊C8) | C2 | semidirect |
| 10. #19104735 | C22 | semidirect |
| 13. #19104668 | C22 | semidirect |
| 14. C4⋊(C163⋊C8) | C22 | semidirect |
| 34. C2×D4×C163 | Q8 | semidirect |
| 58. D4×C163 | C2×Q8 | semidirect |
| 86. C2×C163 | #474 | semidirect |
| 90. C163 | C2×#474 | semidirect |
| 119. C2×D4 | Dic326 | semidirect |
| 146. D4 | C2×Dic326 | semidirect |
| 177. C2 | #23781945 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104735 | 2 |
| #23781945 | 2 |
| C2×#19104668 | 2 |
| C2×C4⋊(C163⋊C8) | 2 |
| C2×#19104656 | 2 |
| C2×C4×D4×C163 | 2 |
| C2×#474 | 163 |