Finite Group DatabasebetaFinite Group Databasebeta← C3×C19×ΓL(1,𝔽8)×Dic7 #45691876
Order 33516.
152 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|
| C2×C3×C7×C19×ΓL(1,𝔽8) | 2 |
| C3×C7×C19×Dic7 | 3 |
| C19×ΓL(1,𝔽8)×Dic7 | 3 |
| C32×C19×Dic7 | 7 |
| C3×C4×C19×ΓL(1,𝔽8) | 7 |
| C3×ΓL(1,𝔽8)×Dic7 | 19 |