Finite Group DatabasebetaFinite Group Databasebeta← C32×C22⋊C4×ΓL(1,𝔽8) #72247155
Order 3024.
952 conjugacy classes of subgroups; only the 374 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 374 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×C32×ΓL(1,𝔽8) | 2 |
| C2×C32×C4×ΓL(1,𝔽8) | 2 |
| C32×C7×C22⋊C4 | 3 |
| C3×C22⋊C4×ΓL(1,𝔽8) | 3 |
| C33×C22⋊C4 | 7 |