Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23781674 | C2 | semidirect |
| 5. #23781426 | C2 | semidirect |
| 6. #23781424 | C2 | semidirect |
| 7. #419×C163 | C2 | semidirect |
| 11. #19104724 | C4 | semidirect |
| 42. C4×Dic163 | C2×C4 | semidirect |
| 48. C2×Q8×C163 | C2×C4 | semidirect |
| 107. C163 | #1885 | semidirect |
| 112. #419 | D163 | semidirect |
| 138. C2×Q8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104724 | 2 |
| #23782139 | 2 |
| #23781674 | 2 |
| C2×#19104651 | 2 |
| #23781426 | 2 |
| #23781424 | 2 |
| #419×C163 | 2 |
| #1885 | 163 |