Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
334 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 334 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 |
|---|---|---|
| 3. #24923277 | C2 | semidirect |
| 4. #24923174 | C2 | semidirect |
| 5. #24923038 | C2 | semidirect |
| 6. #24923028 | C2 | semidirect |
| 10. #19128862 | C4 | semidirect |
| 33. C2×Dic334 | C2×C4 | semidirect |
| 41. #14581934 | C2×C4 | semidirect |
| 124. C167 | #1882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128862 | 2 |
| C2×#19128759 | 2 |
| #24923277 | 2 |
| #24923174 | 2 |
| #24923038 | 2 |
| #24923028 | 2 |
| #520×C167 | 2 |
| #1882 | 167 |