Finite Group DatabasebetaFinite Group DatabasebetaOrder 3024.
580 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 122 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⋊(C3⋊AGL(1,𝔽7)) | 2 |
| C2×C3×C3⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| C2×C3×Dic3×ΓL(1,𝔽8) | 2 |
| #92687⋊C3 | 2 |
| C2×#92687 | 3 |
| C2×C4×C3⋊AGL(1,𝔽7) | 3 |
| C2×(C3⋊AGL(1,𝔽7))⋊C4 | 3 |
| C2×C3×#624 | 7 |