Finite Group DatabasebetaFinite Group DatabasebetaOrder 2688.
708 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|
| D42×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×B(4,𝔽2) | 2 |
| ΓL(1,𝔽8)×#453 | 2 |
| ΓL(1,𝔽8)×#353 | 2 |
| ΓL(1,𝔽8)×AΣL(1,𝔽16) | 2 |
| C7×#2196 | 3 |
| C3×#2196 | 7 |