Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23782143 | C2 | semidirect |
| 3. C2×#19104654 | C2 | semidirect |
| 4. #23781421 | C2 | semidirect |
| 14. C4⋊Q8×C163 | C4 | semidirect |
| 15. #124×C163 | C4 | semidirect |
| 81. C163 | #1912 | semidirect |
| 91. C4⋊Q8 | Dic163 | semidirect |
| 92. #124 | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782143 | 2 |
| #23781682 | 2 |
| C2×#19104654 | 2 |
| #23781421 | 2 |
| #536×C163 | 2 |
| #1912 | 163 |