Finite Group DatabasebetaFinite Group Databasebeta← D5×C22⋊C4×ΓL(1,𝔽8) #72218072
Order 3360.
528 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 147 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×D5×ΓL(1,𝔽8) | 2 |
| C2×C4×D5×ΓL(1,𝔽8) | 2 |
| C5×C22⋊C4×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×C22⋊Dic5 | 2 |
| ΓL(1,𝔽8)×#685 | 2 |
| C7×D5×C22⋊C4 | 3 |
| C2×C22⋊C4×ΓL(1,𝔽8) | 5 |
| C3×D5×C22⋊C4 | 7 |