Finite Group DatabasebetaFinite Group DatabasebetaOrder 3360.
272 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 87 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.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×#709 | 2 |
| ΓL(1,𝔽8)×#687 | 2 |
| ΓL(1,𝔽8)×#686 | 2 |
| ΓL(1,𝔽8)×#681 | 2 |
| C7×#4078 | 3 |
| ΓL(1,𝔽8)×AGL(1,ℤ/8) | 5 |
| C3×#4078 | 7 |