Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19128840 | C2 | semidirect |
| 2. #24923847 | C2 | semidirect |
| 3. #24923836 | C2 | semidirect |
| 4. #24923519 | C2 | semidirect |
| 5. #24923512 | C2 | semidirect |
| 6. #24923502 | C2 | semidirect |
| 7. #24923495 | C2 | semidirect |
| 8. #24923311 | C2 | semidirect |
| 9. #24923265 | C2 | semidirect |
| 10. C2×#19128753 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C167 | C2 | semidirect |
| 14. C2×#14581933 | C22 | semidirect |
| 16. C2×C8×D167 | C22 | semidirect |
| 20. #19128808 | C22 | semidirect |
| 25. #19128803 | C22 | semidirect |
| 29. #19128766 | C22 | semidirect |
| 30. #19128764 | C22 | semidirect |
| 31. #19128756 | C22 | semidirect |
| 32. #19128756 | C22 | semidirect |
| 35. #19128753 | C22 | semidirect |
| 36. #19128753 | C22 | semidirect |
| 83. M16×C167 | D4 | semidirect |
| 151. C167 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D167 | semidirect |
| 220. M16 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128840 | 2 |
| #24923847 | 2 |
| #24923836 | 2 |
| #24923519 | 2 |
| #24923512 | 2 |
| #24923502 | 2 |
| #24923495 | 2 |
| #24923311 | 2 |
| #24923265 | 2 |
| C2×#19128753 | 2 |
| C2×AGL(1,ℤ/8)×C167 | 2 |
| #3062 | 167 |