Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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. #23781553 | C2 | semidirect |
| 4. #23781553 | C2 | semidirect |
| 5. #23781552 | C2 | semidirect |
| 6. #23781516 | C2 | semidirect |
| 7. C22⋊C4×Dic163 | C2 | semidirect |
| 8. C4×C22⋊Dic163 | C2 | semidirect |
| 11. #19104716 | C4 | semidirect |
| 34. C22×Dic163 | C2×C4 | semidirect |
| 41. Dic163⋊C4 | C2×C4 | semidirect |
| 45. C22⋊Dic163 | C2×C4 | semidirect |
| 126. C163 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104716 | 2 |
| #23781568 | 2 |
| #23781553 | 2 |
| #23781552 | 2 |
| #23781516 | 2 |
| C22⋊C4×Dic163 | 2 |
| C4×C22⋊Dic163 | 2 |
| #386×C163 | 2 |
| #2374 | 163 |