Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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. #135×D167 | C2 | semidirect |
| 2. #24923711 | C2 | semidirect |
| 3. #24923708 | C2 | semidirect |
| 4. #24923706 | C2 | semidirect |
| 5. #24923703 | C2 | semidirect |
| 6. #24923701 | C2 | semidirect |
| 7. #24923699 | C2 | semidirect |
| 8. C2×#19128771 | C2 | semidirect |
| 9. #508×C167 | C2 | semidirect |
| 12. #19128854 | C22 | semidirect |
| 16. Q16×D167 | C22 | semidirect |
| 18. D8×D167 | C22 | semidirect |
| 20. Dic1336 | C22 | semidirect |
| 21. #19128778 | C22 | semidirect |
| 22. #19128777 | C22 | semidirect |
| 23. #19128776 | C22 | semidirect |
| 24. #19128775 | C22 | semidirect |
| 25. D2672 | C22 | semidirect |
| 26. #19128773 | C22 | semidirect |
| 27. #19128771 | C22 | semidirect |
| 28. #19128771 | C22 | semidirect |
| 29. C2×C167⋊C16 | C22 | semidirect |
| 30. #135×C167 | C22 | semidirect |
| 31. Q32×C167 | C22 | semidirect |
| 32. SD32×C167 | C22 | semidirect |
| 33. D16×C167 | C22 | semidirect |
| 34. C2×C16×C167 | C22 | semidirect |
| 103. C167 | #3414 | semidirect |
| 112. #508 | D167 | semidirect |
| 120. #135 | C2×D167 | semidirect |
| 127. Q32 | C2×D167 | semidirect |
| 131. SD32 | C2×D167 | semidirect |
| 134. D16 | C2×D167 | semidirect |
| 138. C2×C16 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D167 | 2 |
| #24923711 | 2 |
| #24923708 | 2 |
| #24923706 | 2 |
| #24923703 | 2 |
| #24923701 | 2 |
| #24923699 | 2 |
| C2×#19128771 | 2 |
| #508×C167 | 2 |
| #3414 | 167 |