Finite Group DatabasebetaFinite Group Databasebeta← C3×ΓL(1,𝔽8)×B(4,𝔽2) #72246162
Order 4032.
1188 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1188 conjugacy classes of subgroups — too many to draw. Only its 216 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 |
|---|---|
| C3×ΓL(1,𝔽8)×#99 | 2 |
| C3×ΓL(1,𝔽8)×H(5,𝔽2) | 2 |
| C3×ΓL(1,𝔽8)×#120 | 2 |
| C3×C7×B(4,𝔽2) | 3 |
| ΓL(1,𝔽8)×B(4,𝔽2) | 3 |
| C32×B(4,𝔽2) | 7 |