Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×C7×ΓL(1,𝔽8)×C25 #36347764
Order 22050.
168 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 96 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×C7×ΓL(1,𝔽8)×C25 | 2 |
| C2×C7×ΓL(1,𝔽8)×C25 | 3 |
| C2×C3×C72×C25 | 3 |
| C2×C3×C5×C7×ΓL(1,𝔽8) | 5 |
| C2×C3×ΓL(1,𝔽8)×C25 | 7 |
| C2×C32×C7×C25 | 7 |