Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
994 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 173 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. #24923780 | C2 | semidirect |
| 3. #24923420 | C2 | semidirect |
| 4. #24923403 | C2 | semidirect |
| 5. #24923274 | C2 | semidirect |
| 6. #24923233 | C2 | semidirect |
| 7. C23×D4×C167 | C2 | semidirect |
| 8. C2×#14581950 | C22 | semidirect |
| 10. C2×#14581938 | C22 | semidirect |
| 11. C2×#14581935 | C22 | semidirect |
| 12. C2×#14581934 | C22 | semidirect |
| 14. #19128811 | C22 | semidirect |
| 15. #19128806 | C22 | semidirect |
| 18. #19128791 | C22 | semidirect |
| 19. #19128753 | C22 | semidirect |
| 20. C22⋊(C167⋊C8) | C22 | semidirect |
| 29. C2×Dic334 | C23 | semidirect |
| 30. C2×D668 | C23 | semidirect |
| 37. C2×C167⋊C8 | C23 | semidirect |
| 38. C4⋊Dic167 | C23 | semidirect |
| 55. C2×D4×C167 | D4 | semidirect |
| 102. C22×C167 | AGL(1,ℤ/8) | semidirect |
| 117. C167 | #3003 | semidirect |
| 119. C23×D4 | D167 | semidirect |
| 162. C2×D4 | C22⋊D167 | semidirect |
| 222. C22 | #19128858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128858 | 2 |
| #24923780 | 2 |
| #24923420 | 2 |
| #24923403 | 2 |
| #24923274 | 2 |
| #24923233 | 2 |
| C23×D4×C167 | 2 |
| #3003 | 167 |