Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #24923979 | C2 | semidirect |
| 3. #24923616 | C2 | semidirect |
| 4. #24923589 | C2 | semidirect |
| 5. #24923559 | C2 | semidirect |
| 6. #24923501 | C2 | semidirect |
| 7. #24923469 | C2 | semidirect |
| 8. #24923418 | C2 | semidirect |
| 9. C8×D668 | C2 | semidirect |
| 10. #102×D167 | C2 | semidirect |
| 11. C4×SD16×C167 | C2 | semidirect |
| 14. C2×#14581937 | C22 | semidirect |
| 15. C2×C8×D167 | C22 | semidirect |
| 16. #19128832 | C22 | semidirect |
| 20. #19128808 | C22 | semidirect |
| 26. C4⋊C4×D167 | C22 | semidirect |
| 27. #19128763 | C22 | semidirect |
| 28. C4⋊(C167⋊C8) | C22 | semidirect |
| 29. #19128754 | C22 | semidirect |
| 30. #19128754 | C22 | semidirect |
| 32. #19128752 | C22 | semidirect |
| 33. (C2×D167)⋊C8 | C22 | semidirect |
| 35. C4×Q8×C167 | C22 | semidirect |
| 37. #106×C167 | C22 | semidirect |
| 38. #103×C167 | C22 | semidirect |
| 40. C4×C8×C167 | C22 | semidirect |
| 88. D668 | SD16 | semidirect |
| 136. C167 | #3295 | semidirect |
| 146. C4×SD16 | D167 | semidirect |
| 162. C4×Q8 | C2×D167 | semidirect |
| 168. #106 | C2×D167 | semidirect |
| 170. #103 | C2×D167 | semidirect |
| 177. C4×C8 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923979 | 2 |
| D4×D668 | 2 |
| #24923616 | 2 |
| #24923589 | 2 |
| #24923559 | 2 |
| #24923501 | 2 |
| #24923469 | 2 |
| #24923418 | 2 |
| C8×D668 | 2 |
| #102×D167 | 2 |
| C4×SD16×C167 | 2 |
| #3295 | 167 |