Finite Group DatabasebetaFinite Group DatabasebetaOrder 3024.
580 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|
| C22×C3⋊D3×ΓL(1,𝔽8) | 2 |
| C2×C3×Dic3×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×#624 | 2 |
| C2×C7×#624 | 3 |
| C2×C4×D3×ΓL(1,𝔽8) | 3 |
| C2×C3×#624 | 7 |