Finite Group DatabasebetaFinite Group Databasebeta← C3×C29×C3⋊(C7⋊AGL(1,𝔽5)) #49141566
Order 36540.
112 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|
| C32×C7×D5×C29 | 2 |
| C29×C3⋊(C7⋊AGL(1,𝔽5)) | 3 |
| C3×C29×C7⋊AGL(1,𝔽5) | 3 |
| C3×C29×Dic21 | 5 |
| C3×C29×ΓL(1,𝔽16) | 7 |
| C3×C3⋊(C7⋊AGL(1,𝔽5)) | 29 |