Finite Group DatabasebetaFinite Group Databasebeta← C5×Dic3×C17×ΓL(1,𝔽8) #36339307
Order 21420.
112 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 60 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×C5×C17×ΓL(1,𝔽8) | 2 |
| C5×C7×Dic3×C17 | 3 |
| C4×C5×C17×ΓL(1,𝔽8) | 3 |
| Dic3×C17×ΓL(1,𝔽8) | 5 |
| C3×C5×Dic3×C17 | 7 |
| C5×Dic3×ΓL(1,𝔽8) | 17 |