Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
852 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 173 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×Q8×D163 | C2 | semidirect |
| 2. C2×#19104722 | C2 | semidirect |
| 4. #23781577 | C2 | semidirect |
| 5. #23781572 | C2 | semidirect |
| 6. #23781571 | C2 | semidirect |
| 7. #23781541 | C2 | semidirect |
| 8. C4×(C2×D163)⋊C4 | C2 | semidirect |
| 9. C2×#124×C163 | C2 | semidirect |
| 39. C2×Dic326 | D4 | semidirect |
| 61. C2×Q8×C163 | D4 | semidirect |
| 122. C2×D163 | #124 | semidirect |
| 137. C163 | #2436 | semidirect |
| 141. C2×#124 | D163 | semidirect |
| 182. C2×Q8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D163 | 2 |
| C2×#19104722 | 2 |
| C2×#19104706 | 2 |
| #23781577 | 2 |
| #23781572 | 2 |
| #23781571 | 2 |
| #23781541 | 2 |
| C4×(C2×D163)⋊C4 | 2 |
| C2×#124×C163 | 2 |
| #2436 | 163 |