Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
5872 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.
This group has 5872 conjugacy classes of subgroups — too many to draw. Only its 3213 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×#19128880 | C2 | semidirect |
| 2. C2×#19128879 | C2 | semidirect |
| 3. 2−1+4×D167 | C2 | direct (N × H) |
| 4. C2×#41×D167 | C2 | semidirect |
| 5. C22×Q8×D167 | C2 | semidirect |
| 6. C2×2−1+4×C167 | C2 | semidirect |
| 7. #19128880 | C22 | semidirect |
| 8. #19128879 | C22 | semidirect |
| 9. C2×#14581951 | C22 | semidirect |
| 10. C2×#14581950 | C22 | semidirect |
| 11. C2×#14581949 | C22 | semidirect |
| 12. #41×D167 | C22 | semidirect |
| 13. C22×Dic334 | C22 | semidirect |
| 15. C2×Q8×D167 | C22 | semidirect |
| 16. C2×Q8×D167 | C22 | semidirect |
| 19. 2−1+4×C167 | C22 | semidirect |
| 20. C2×#41×C167 | C22 | semidirect |
| 21. C22×Q8×C167 | C22 | semidirect |
| 23. #14581951 | C23 | semidirect |
| 24. #14581950 | C23 | semidirect |
| 25. #14581949 | C23 | semidirect |
| 27. C2×Dic334 | C23 | semidirect |
| 29. Q8×D167 | C23 | semidirect |
| 37. #41×C167 | C23 | semidirect |
| 39. C2×Q8×C167 | C23 | semidirect |
| 63. C2×D167 | 2−1+4 | direct (N × H) |
| 69. C2×C167 | C2×2−1+4 | semidirect |
| 72. D167 | C2×2−1+4 | direct (N × H) |
| 73. C167 | C22×2−1+4 | semidirect |
| 78. C2×2−1+4 | D167 | direct (N × H) |
| 83. 2−1+4 | C2×D167 | direct (N × H) |
| 88. C2×#41 | C2×D167 | semidirect |
| 93. C22×Q8 | C2×D167 | semidirect |
| 100. #41 | C22×D167 | semidirect |
| 106. C2×Q8 | C22×D167 | semidirect |
| 145. C2 | 2−1+4×D167 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128880 | 2 |
| C2×#19128879 | 2 |
| 2−1+4×D167 | 2 |
| C2×#41×D167 | 2 |
| C22×Q8×D167 | 2 |
| C2×2−1+4×C167 | 2 |
| C22×2−1+4 | 167 |