Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
1324 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 315 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 |
|---|---|
| C25×ΓL(1,𝔽8) | 2 |
| C22×D4×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×#120 | 2 |
| C2×C22⋊C4×ΓL(1,𝔽8) | 2 |
| C2×C7×#120 | 3 |
| C2×C3×#120 | 7 |