Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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. M32×D167 | C2 | semidirect |
| 3. #106×D167 | C2 | semidirect |
| 4. #24923080 | C2 | semidirect |
| 5. #24923079 | C2 | semidirect |
| 6. #24923078 | C2 | semidirect |
| 7. #360×C167 | C2 | semidirect |
| 9. #19128855 | C4 | semidirect |
| 13. #19128851 | C4 | semidirect |
| 14. Q16×D167 | C4 | semidirect |
| 16. D8×D167 | C4 | semidirect |
| 19. #19128772 | C22 | semidirect |
| 22. #19128764 | C22 | semidirect |
| 25. M32×C167 | C22 | semidirect |
| 26. #106×C167 | C22 | semidirect |
| 38. Dic668 | C2×C4 | semidirect |
| 43. D1336 | C2×C4 | semidirect |
| 54. Q16×C167 | C2×C4 | semidirect |
| 56. D8×C167 | C2×C4 | semidirect |
| 110. D167 | #360 | direct (N × H) |
| 111. C167 | C2×#360 | semidirect |
| 119. #360 | D167 | direct (N × H) |
| 134. M32 | C2×D167 | semidirect |
| 138. #106 | C2×D167 | semidirect |
| 153. Q16 | C4×D167 | semidirect |
| 160. D8 | C4×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D167 | 2 |
| M32×D167 | 2 |
| #106×D167 | 2 |
| #24923080 | 2 |
| #24923079 | 2 |
| #24923078 | 2 |
| #360×C167 | 2 |
| C2×#360 | 167 |