Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19128856 | C2 | semidirect |
| 2. #24923914 | C2 | semidirect |
| 3. #24923653 | C2 | semidirect |
| 4. #24923516 | C2 | semidirect |
| 5. #24923484 | C2 | semidirect |
| 6. #24923432 | C2 | semidirect |
| 7. #24923404 | C2 | semidirect |
| 8. #24923348 | C2 | semidirect |
| 9. C4×D8×C167 | C2 | semidirect |
| 11. C2×D4×D167 | C22 | semidirect |
| 13. C2×Dic668 | C22 | semidirect |
| 14. C2×#14581939 | C22 | semidirect |
| 15. C2×#14581938 | C22 | semidirect |
| 18. C2×#14581933 | C22 | semidirect |
| 19. #19128820 | C22 | semidirect |
| 21. #19128812 | C22 | semidirect |
| 27. C4⋊(C167⋊C8) | C22 | semidirect |
| 28. #19128755 | C22 | semidirect |
| 29. #19128752 | C22 | semidirect |
| 30. (C2×D167)⋊C8 | C22 | semidirect |
| 32. C4×D4×C167 | C22 | semidirect |
| 33. #107×C167 | C22 | semidirect |
| 34. #102×C167 | C22 | semidirect |
| 35. C4×C8×C167 | C22 | semidirect |
| 65. D8×C167 | D4 | semidirect |
| 124. C167 | #3273 | semidirect |
| 133. C4×D8 | D167 | semidirect |
| 152. C4×D4 | C2×D167 | semidirect |
| 154. #107 | C2×D167 | semidirect |
| 158. #102 | C2×D167 | semidirect |
| 160. C4×C8 | C2×D167 | semidirect |
| 181. D8 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128856 | 2 |
| #24923914 | 2 |
| #24923653 | 2 |
| #24923516 | 2 |
| #24923484 | 2 |
| #24923432 | 2 |
| #24923404 | 2 |
| #24923348 | 2 |
| C4×D8×C167 | 2 |
| #3273 | 167 |