Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19128878 | C2 | semidirect |
| 2. C22×#14581935 | C2 | semidirect |
| 3. #24923836 | C2 | semidirect |
| 4. #24923413 | C2 | semidirect |
| 5. #24923401 | C2 | semidirect |
| 6. #24923275 | C2 | semidirect |
| 7. #24923265 | C2 | semidirect |
| 8. #24923237 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C167 | C2 | semidirect |
| 12. C2×#14581951 | C22 | semidirect |
| 18. C2×D4×D167 | C22 | semidirect |
| 20. C2×#14581935 | C22 | semidirect |
| 21. C22×C167⋊C8 | C22 | semidirect |
| 24. #19128803 | C22 | semidirect |
| 26. #19128791 | C22 | semidirect |
| 27. #19128756 | C22 | semidirect |
| 28. #19128754 | C22 | semidirect |
| 29. #19128753 | C22 | semidirect |
| 30. (C2×D167)⋊C8 | C22 | semidirect |
| 32. C22×D4×C167 | C22 | semidirect |
| 34. C2×SD16×C167 | C22 | semidirect |
| 35. C2×D8×C167 | C22 | semidirect |
| 36. C2×M16×C167 | C22 | semidirect |
| 50. C2×D668 | D4 | semidirect |
| 69. #41×C167 | D4 | semidirect |
| 151. C167 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D167 | semidirect |
| 172. C22×D4 | C2×D167 | semidirect |
| 174. C2×SD16 | C2×D167 | semidirect |
| 177. C2×D8 | C2×D167 | semidirect |
| 178. C2×M16 | C2×D167 | semidirect |
| 198. #41 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128878 | 2 |
| C22×#14581935 | 2 |
| #24923836 | 2 |
| #24923413 | 2 |
| #24923401 | 2 |
| #24923275 | 2 |
| #24923265 | 2 |
| #24923237 | 2 |
| C2×AGL(1,ℤ/8)×C167 | 2 |
| #3008 | 167 |