Finite Group DatabasebetaFinite Group DatabasebetaOrder 1680.
160 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 64 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. C3×C22⋊D35 | C2 | semidirect |
| 2. C2×C3×C7×Dic5 | C2 | semidirect |
| 3. C3×C5×C22⋊D7 | C2 | semidirect |
| 4. C3×#63308 | C2 | semidirect |
| 5. C3×#63306 | C2 | semidirect |
| 6. C3×#63304 | C2 | semidirect |
| 7. C3×D7×Dic5 | C2 | semidirect |
| 8. #10587952 | C3 | direct (N × H) |
| 17. C22⋊D35 | C2×C3 | semidirect |
| 18. C2×C7×Dic5 | C2×C3 | semidirect |
| 19. C5×C22⋊D7 | C2×C3 | semidirect |
| 20. #63308 | C2×C3 | semidirect |
| 21. #63306 | C2×C3 | semidirect |
| 22. #63304 | C2×C3 | semidirect |
| 23. D7×Dic5 | C2×C3 | semidirect |
| 31. C3×C22⋊D7 | D5 | semidirect |
| 47. C2×C3×Dic5 | D7 | semidirect |
| 51. C3×C5×C7 | #41 | semidirect |
| 73. C22⋊D7 | C3×D5 | semidirect |
| 87. C2×Dic5 | C3×D7 | semidirect |
| 90. C5×C7 | C3×#41 | semidirect |
| 109. C3×C7 | #711 | semidirect |
| 118. C3×C5 | #1157 | semidirect |
| 141. C7 | C3×#711 | semidirect |
| 146. C5 | C3×#1157 | semidirect |
| 154. C3 | #10587952 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C22⋊D35 | 2 |
| C2×C3×C7×Dic5 | 2 |
| C3×C5×C22⋊D7 | 2 |
| C3×#63308 | 2 |
| C3×#63306 | 2 |
| C3×#63304 | 2 |
| C3×D7×Dic5 | 2 |
| #10587952 | 3 |
| C3×#1157 | 5 |
| C3×#711 | 7 |