Finite Group DatabasebetaFinite Group DatabasebetaOrder 1680.
136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 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×C3⋊(C7⋊AGL(1,𝔽5)) | C2 | semidirect |
| 3. C2×C7×ΓL(1,𝔽16) | C2 | semidirect |
| 5. C2×C3×D35 | C4 | semidirect |
| 7. C2×C3×C5×D7 | C4 | semidirect |
| 25. C2×D35 | Dic3 | semidirect |
| 27. C2×C5×D7 | Dic3 | semidirect |
| 34. C2×ΓL(1,𝔽16) | D7 | semidirect |
| 36. C3×C5×C7 | C22⋊C4 | semidirect |
| 41. C2×C3×D7 | AGL(1,𝔽5) | semidirect |
| 69. C5×C7 | #217 | semidirect |
| 79. C2×D7 | ΓL(1,𝔽16) | semidirect |
| 85. C3×C7 | C22⋊AGL(1,𝔽5) | semidirect |
| 94. C3×C5 | (C2×D7)⋊C4 | semidirect |
| 115. C7 | #6763 | semidirect |
| 121. C5 | (C2×D7)⋊Dic3 | semidirect |
| 129. C3 | (C2×D7)⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D5×D7 | 2 |
| C2×C3⋊(C7⋊AGL(1,𝔽5)) | 2 |
| C2×C7×ΓL(1,𝔽16) | 2 |
| (C2×D7)⋊AGL(1,𝔽5) | 3 |
| (C2×D7)⋊Dic3 | 5 |
| #6763 | 7 |