Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19128860 | C2 | semidirect |
| 2. C2×#19128852 | C2 | semidirect |
| 3. C22×#14581935 | C2 | semidirect |
| 4. #24923836 | C2 | semidirect |
| 5. #24923833 | C2 | semidirect |
| 6. #24923657 | C2 | semidirect |
| 7. #24923655 | C2 | semidirect |
| 8. #24923650 | C2 | semidirect |
| 9. #24923644 | C2 | semidirect |
| 10. #24923227 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C167 | C2 | semidirect |
| 16. C2×#14581940 | C22 | semidirect |
| 17. C2×#14581939 | C22 | semidirect |
| 18. C2×#14581938 | C22 | semidirect |
| 19. C2×#14581937 | C22 | semidirect |
| 20. C2×D1336 | C22 | semidirect |
| 24. C2×#14581935 | C22 | semidirect |
| 26. #19128828 | C22 | semidirect |
| 27. #19128828 | C22 | semidirect |
| 28. #19128821 | C22 | semidirect |
| 29. #19128819 | C22 | semidirect |
| 35. #19128742 | C22 | semidirect |
| 36. C8×Dic167 | C22 | semidirect |
| 40. C2×SD16×C167 | C22 | semidirect |
| 41. C2×D8×C167 | C22 | semidirect |
| 64. C2×C167⋊C8 | D4 | semidirect |
| 86. M16×C167 | D4 | semidirect |
| 153. C167 | #3155 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D167 | semidirect |
| 177. C2×SD16 | C2×D167 | semidirect |
| 183. C2×D8 | C2×D167 | semidirect |
| 232. M16 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128860 | 2 |
| C2×#19128852 | 2 |
| C22×#14581935 | 2 |
| #24923836 | 2 |
| #24923833 | 2 |
| #24923657 | 2 |
| #24923655 | 2 |
| #24923650 | 2 |
| #24923644 | 2 |
| #24923227 | 2 |
| C2×AGL(1,ℤ/8)×C167 | 2 |
| #3155 | 167 |