Finite Group DatabasebetaFinite Group DatabasebetaOrder 1680.
136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 2. C2×C7×ΓL(1,𝔽16) | C2 | semidirect |
| 4. C22×C3×C5×C7 | C4 | semidirect |
| 6. C2×C3×C7×D5 | C4 | semidirect |
| 12. #6763 | C7 | direct (N × H) |
| 19. C22×C5×C7 | Dic3 | semidirect |
| 21. C2×C7×D5 | Dic3 | semidirect |
| 25. C2×ΓL(1,𝔽16) | C2×C7 | semidirect |
| 27. C3×C5×C7 | C22⋊C4 | semidirect |
| 31. C22×C3×C7 | AGL(1,𝔽5) | semidirect |
| 38. C22×C3×C5 | C4×C7 | semidirect |
| 40. C2×C3×D5 | C4×C7 | semidirect |
| 52. C5×C7 | #217 | semidirect |
| 60. C22×C7 | ΓL(1,𝔽16) | semidirect |
| 64. C3×C7 | C22⋊AGL(1,𝔽5) | semidirect |
| 65. C22×C5 | C7×Dic3 | semidirect |
| 67. C2×D5 | C7×Dic3 | semidirect |
| 71. C3×C5 | C7×C22⋊C4 | semidirect |
| 79. C22×C3 | C7×AGL(1,𝔽5) | semidirect |
| 87. C7 | #6763 | direct (N × H) |
| 92. C5 | C7×#217 | semidirect |
| 96. C22 | C7×ΓL(1,𝔽16) | semidirect |
| 98. C3 | C7×C22⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×D5 | 2 |
| C2×C7×ΓL(1,𝔽16) | 2 |
| C7×C22⋊AGL(1,𝔽5) | 3 |
| C7×#217 | 5 |
| #6763 | 7 |