Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19128858 | C2 | semidirect |
| 2. C2×#19128838 | C2 | semidirect |
| 3. #24923850 | C2 | semidirect |
| 4. #24923836 | C2 | semidirect |
| 5. #24923521 | C2 | semidirect |
| 6. #24923514 | C2 | semidirect |
| 7. #24923504 | C2 | semidirect |
| 8. #24923497 | C2 | semidirect |
| 9. #24923309 | C2 | semidirect |
| 10. #24923266 | C2 | semidirect |
| 11. C2×#102×C167 | C2 | semidirect |
| 19. C2×#14581933 | C22 | semidirect |
| 20. C2×C8×D167 | C22 | semidirect |
| 24. #19128812 | C22 | semidirect |
| 26. #19128807 | C22 | semidirect |
| 32. #19128765 | C22 | semidirect |
| 33. #19128763 | C22 | semidirect |
| 34. #19128757 | C22 | semidirect |
| 35. #19128757 | C22 | semidirect |
| 36. #19128754 | C22 | semidirect |
| 37. #19128754 | C22 | semidirect |
| 60. #14581934 | D4 | semidirect |
| 151. C167 | #3062 | semidirect |
| 163. C2×#102 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128858 | 2 |
| C2×#19128838 | 2 |
| #24923850 | 2 |
| #24923836 | 2 |
| #24923521 | 2 |
| #24923514 | 2 |
| #24923504 | 2 |
| #24923497 | 2 |
| #24923309 | 2 |
| #24923266 | 2 |
| C2×#102×C167 | 2 |
| #3062 | 167 |