Finite Group DatabasebetaFinite Group Databasebeta← C3×C7×C17×ΓL(1,𝔽8)⋊C4 #44472643
Order 29988.
152 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 88 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×C17×ΓL(1,𝔽8) | 2 |
| C3×C7×C17×Dic7 | 3 |
| C7×C17×ΓL(1,𝔽8)⋊C4 | 3 |
| C3×C17×ΓL(1,𝔽8)⋊C4 | 7 |
| C32×C4×C7×C17 | 7 |
| C3×C7×ΓL(1,𝔽8)⋊C4 | 17 |