Finite Group DatabasebetaFinite Group DatabasebetaOrder 1680.
216 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 75 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. C23×C3×C5×C7 | C2 | semidirect |
| 2. C22×D105 | C2 | semidirect |
| 3. #11719828 | C2 | direct (N × H) |
| 4. C2×Dic105 | C2 | semidirect |
| 8. C22×C3×C5×C7 | C22 | semidirect |
| 10. C2×D105 | C22 | semidirect |
| 11. Dic105 | C22 | semidirect |
| 13. C23×C5×C7 | D3 | semidirect |
| 19. C2×C3×C5×C7 | D4 | semidirect |
| 22. C23×C3×C7 | D5 | semidirect |
| 28. C22×C5×C7 | C2×D3 | semidirect |
| 32. C23×C3×C5 | D7 | semidirect |
| 37. C3×C5×C7 | C2×D4 | semidirect |
| 40. C22×C3×C7 | C2×D5 | semidirect |
| 46. C2×C5×C7 | #67 | semidirect |
| 51. C22×C3×C5 | C2×D7 | semidirect |
| 55. C23×C7 | D15 | semidirect |
| 61. C2×C3×C7 | C22⋊D5 | semidirect |
| 64. C23×C5 | D21 | semidirect |
| 68. C5×C7 | C2×#67 | semidirect |
| 70. C2×C3×C5 | C22⋊D7 | semidirect |
| 75. C22×C7 | C2×D15 | semidirect |
| 79. C23×C3 | D35 | semidirect |
| 83. C3×C7 | C2×C22⋊D5 | semidirect |
| 86. C22×C5 | C2×D21 | semidirect |
| 91. C3×C5 | C2×C22⋊D7 | semidirect |
| 93. C2×C7 | #1220 | semidirect |
| 98. C22×C3 | C2×D35 | semidirect |
| 103. C2×C5 | #4268 | semidirect |
| 107. C23 | D105 | semidirect |
| 110. C7 | C2×#1220 | semidirect |
| 112. C2×C3 | C22⋊D35 | semidirect |
| 115. C5 | C2×#4268 | semidirect |
| 120. C22 | C2×D105 | semidirect |
| 122. C3 | C2×C22⋊D35 | semidirect |
| 125. C2 | #11719828 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C5×C7 | 2 |
| C22×D105 | 2 |
| #11719828 | 2 |
| C2×Dic105 | 2 |
| C2×C22⋊D35 | 3 |
| C2×#4268 | 5 |
| C2×#1220 | 7 |