Finite Group DatabasebetaFinite Group Databasebeta← C3×C7×C13×C7⋊AGL(1,𝔽5) #50304355
Order 38220.
144 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 56 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×C72×D5×C13 | 2 |
| C7×C13×C7⋊AGL(1,𝔽5) | 3 |
| C3×C7×C13×Dic7 | 5 |
| C3×C13×C7⋊AGL(1,𝔽5) | 7 |
| C3×C7×C13×AGL(1,𝔽5) | 7 |
| C3×C7×C7⋊AGL(1,𝔽5) | 13 |