Finite Group DatabasebetaFinite Group DatabasebetaOrder 3360.
520 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 96 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×(C22⋊D35)⋊C3 | 2 |
| (C22⋊Dic35)⋊C3 | 2 |
| #10587902⋊C3 | 2 |
| #11765269 | 3 |
| #6500⋊C3 | 5 |
| C3×#4083 | 7 |