Finite Group DatabasebetaFinite Group DatabasebetaOrder 1680.
136 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 45 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×Dic5×ΓL(1,𝔽8) | C2 | semidirect |
| 3. C2×C5×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 4. #10587856 | C3 | semidirect |
| 8. C2×C5⋊AGL(1,𝔽7) | C4 | semidirect |
| 13. C2×C7×Dic5 | C2×C3 | semidirect |
| 14. C2×C5×Dic7 | C2×C3 | semidirect |
| 22. C2×ΓL(1,𝔽8)⋊C4 | D5 | semidirect |
| 26. C2×D35 | C3×C4 | semidirect |
| 33. C5×ΓL(1,𝔽8) | C22⋊C4 | semidirect |
| 53. C2×Dic7 | C3×D5 | semidirect |
| 61. C2×Dic5 | AGL(1,𝔽7) | semidirect |
| 62. C5×C7 | C3×C22⋊C4 | semidirect |
| 76. ΓL(1,𝔽8) | #685 | semidirect |
| 102. C7 | C3×#685 | semidirect |
| 107. C5 | (C2×AGL(1,𝔽7))⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5⋊AGL(1,𝔽7) | 2 |
| C2×Dic5×ΓL(1,𝔽8) | 2 |
| C2×C5×ΓL(1,𝔽8)⋊C4 | 2 |
| #10587856 | 3 |
| (C2×AGL(1,𝔽7))⋊C4 | 5 |
| C3×#685 | 7 |