Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #24923292 | C2 | semidirect |
| 3. C2×#19128760 | C2 | semidirect |
| 4. C2×#19128759 | C2 | semidirect |
| 5. C2×#19128758 | C2 | semidirect |
| 6. C42×Dic167 | C2 | semidirect |
| 7. C2×#104×C167 | C2 | semidirect |
| 10. #19128830 | C4 | semidirect |
| 11. #19128828 | C4 | semidirect |
| 12. #19128821 | C4 | semidirect |
| 13. #19128819 | C4 | semidirect |
| 49. C4×Dic167 | D4 | semidirect |
| 64. C42×C167 | D4 | semidirect |
| 119. Dic167 | #104 | semidirect |
| 126. C167 | #1962 | semidirect |
| 133. C2×#104 | D167 | semidirect |
| 191. C42 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923815 | 2 |
| #24923292 | 2 |
| C2×#19128760 | 2 |
| C2×#19128759 | 2 |
| C2×#19128758 | 2 |
| C42×Dic167 | 2 |
| C2×#104×C167 | 2 |
| #1962 | 167 |