Finite Group DatabasebetaFinite Group DatabasebetaOrder 3360.
520 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 126 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×C5×AGL(1,𝔽7) | 2 |
| C2×C5×D4×ΓL(1,𝔽8) | 2 |
| C2×C5×(C22⋊D7)⋊C3 | 2 |
| C5×(C22⋊Dic7)⋊C3 | 2 |
| C5×(C2×AGL(1,𝔽7))⋊C4 | 2 |
| C5×#6500 | 3 |
| #6500⋊C3 | 5 |
| C3×C5×#120 | 7 |