Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
852 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 240 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 |
|---|---|
| C23×C4×ΓL(1,𝔽8) | 2 |
| C22×(C22⋊D7)⋊C3 | 2 |
| C22×C4⋊AGL(1,𝔽7) | 2 |
| #6493⋊C3 | 2 |
| C2×(C2×AGL(1,𝔽7))⋊C4 | 2 |
| C2×C4⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| C2×#6493 | 3 |
| C2×C3×#121 | 7 |