Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×C167⋊#95 | C2 | semidirect |
| 3. #24923007 | C2 | semidirect |
| 4. #24923004 | C2 | semidirect |
| 5. #407×C167 | C2 | semidirect |
| 6. C2×#14581950 | C4 | semidirect |
| 9. #19128811 | C4 | semidirect |
| 11. #19128806 | C4 | semidirect |
| 16. #19128791 | C4 | semidirect |
| 24. C2×Dic334 | C2×C4 | semidirect |
| 25. C2×D668 | C2×C4 | semidirect |
| 34. C4⋊Dic167 | C2×C4 | semidirect |
| 35. C4⋊Dic167 | C2×C4 | semidirect |
| 119. C167 | #1504 | semidirect |
| 122. #407 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923780 | 2 |
| C2×C167⋊#95 | 2 |
| #24923007 | 2 |
| #24923004 | 2 |
| #407×C167 | 2 |
| #1504 | 167 |