Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #24923617 | C2 | semidirect |
| 3. #24923587 | C2 | semidirect |
| 4. #24923556 | C2 | semidirect |
| 5. #24923500 | C2 | semidirect |
| 6. #24923469 | C2 | semidirect |
| 7. #24923419 | C2 | semidirect |
| 8. C4×#14581937 | C2 | semidirect |
| 9. D4×C167⋊C8 | C2 | semidirect |
| 10. C2×#19128752 | C2 | semidirect |
| 11. #554×C167 | C2 | semidirect |
| 15. C2×#14581937 | C22 | semidirect |
| 16. C22×C167⋊C8 | C22 | semidirect |
| 22. #19128763 | C22 | semidirect |
| 23. #19128763 | C22 | semidirect |
| 24. C4⋊(C167⋊C8) | C22 | semidirect |
| 25. #19128756 | C22 | semidirect |
| 28. #19128752 | C22 | semidirect |
| 29. #19128752 | C22 | semidirect |
| 30. #19128752 | C22 | semidirect |
| 31. C22⋊(C167⋊C8) | C22 | semidirect |
| 32. C4×C167⋊C8 | C22 | semidirect |
| 33. C4⋊Q8×C167 | C22 | semidirect |
| 36. C22⋊Q8×C167 | C22 | semidirect |
| 37. C4×Q8×C167 | C22 | semidirect |
| 40. C2×C4⋊C4×C167 | C22 | semidirect |
| 99. D4×C167 | SD16 | semidirect |
| 136. C167 | #3295 | semidirect |
| 138. #554 | D167 | semidirect |
| 154. C4⋊Q8 | C2×D167 | semidirect |
| 158. C22⋊Q8 | C2×D167 | semidirect |
| 162. C4×Q8 | C2×D167 | semidirect |
| 166. C2×C4⋊C4 | C2×D167 | semidirect |
| 231. D4 | #14581937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D668 | 2 |
| #24923617 | 2 |
| #24923587 | 2 |
| #24923556 | 2 |
| #24923500 | 2 |
| #24923469 | 2 |
| #24923419 | 2 |
| C4×#14581937 | 2 |
| D4×C167⋊C8 | 2 |
| C2×#19128752 | 2 |
| #554×C167 | 2 |
| #3295 | 167 |