Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 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. C2×C4×D668 | C2 | semidirect |
| 2. #24923597 | C2 | semidirect |
| 3. #24923580 | C2 | semidirect |
| 4. #24923566 | C2 | semidirect |
| 5. #24923481 | C2 | semidirect |
| 6. #24923419 | C2 | semidirect |
| 8. #24923379 | C2 | semidirect |
| 9. #24923367 | C2 | semidirect |
| 10. #24923326 | C2 | semidirect |
| 11. #529×C167 | C2 | semidirect |
| 22. #19128765 | C22 | semidirect |
| 23. #19128763 | C22 | semidirect |
| 24. C4⋊(C167⋊C8) | C22 | semidirect |
| 25. #19128756 | C22 | semidirect |
| 26. #19128753 | C22 | semidirect |
| 31. #19128743 | C22 | semidirect |
| 33. #125×C167 | C22 | semidirect |
| 34. #124×C167 | C22 | semidirect |
| 38. C4×Q8×C167 | C22 | semidirect |
| 40. C4×D4×C167 | C22 | semidirect |
| 140. C167 | #3114 | semidirect |
| 142. #529 | D167 | semidirect |
| 158. #125 | C2×D167 | semidirect |
| 159. #124 | C2×D167 | semidirect |
| 163. C4×Q8 | C2×D167 | semidirect |
| 169. C4×D4 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D668 | 2 |
| #24923597 | 2 |
| #24923580 | 2 |
| #24923566 | 2 |
| #24923481 | 2 |
| #24923419 | 2 |
| #24923402 | 2 |
| #24923379 | 2 |
| #24923367 | 2 |
| #24923326 | 2 |
| #529×C167 | 2 |
| #3114 | 167 |